# Items where Author is "Higham, Nicholas J."

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Number of items: 273.

## Article

Higham, Nicholas J. and Mary, Theo (2019) A New Approach to Probabilistic Rounding Error Analysis. SIAM Journal on Scientific Computing, 41 (5). A2815-A2835. ISSN 1095-7197

Fasi, Massimiliano and Higham, Nicholas J. (2018) Multiprecision Algorithms for Computing the Matrix Logarithm. SIAM Journal On Matrix Analysis And Applications, 39 (1). pp. 472-491. ISSN 1095-7162

Carson, Erin and Higham, Nicholas J. (2017) A New Analysis of Iterative Refinement and its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems. SIAM Journal on Scientific Computing, 39 (6). A2834-A2856. ISSN 1095-7197

Higham, Nicholas J. and Kandolf, Peter (2017) Computing the Action of Trigonometric and Hyperbolic Matrix Functions. SIAM Journal on Scientific Computing, 39 (2). A613-A627. ISSN 1095-7197

Carson, Erin and Higham, Nicholas J. (2017) Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions. SIAM Journal on Scientific Computing (2017.24). ISSN 1749-9097

Dongarra, Jack and Hammarling, Sven and Higham, Nicholas J. and Relton, Samuel D. and Valero-Lara, Pedro and Zounon, Mawussi (2017) The Design and Performance of Batched BLAS on Modern High-Performance Computing Systems. Procedia Computer Science, 108. pp. 495-504.

Higham, Nicholas J. and Relton, Samuel D. (2016) Estimating the Largest Elements of a Matrix. SIAM Journal on Scientific Computing, 38 (5). C584-C601.

Aprahamian, Mary and Higham, Nicholas J. (2016) Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms. SIAM Journal on Matrix Analysis and Applications, 37 (4). pp. 1453-1477. ISSN 1095-7162

Higham, Nicholas J. and Strabić, Nataša (2016) Bounds for the Distance to the Nearest Correlation Matrix. SIAM Journal on Matrix Analysis and Applications, 37 (3). pp. 1088-1102. ISSN 1095-7162

Higham, Nicholas J. and Strabić, Nataša (2016) Anderson Acceleration of the Alternating Projections Method for Computing the Nearest Correlation Matrix. Numerical Algorithms, 72 (4). pp. 1021-1042. ISSN 1572-9265

Higham, Nicholas J. and Strabić, Nataša and Šego, Vedran (2016) Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block. SIAM Review, 58 (2). pp. 245-263. ISSN 1095-7200

Zhang, Weijian and Higham, Nicholas J. (2016) Matrix Depot: An Extensible Test Matrix Collection for Julia. PeerJ Computer Science, 2. e58. ISSN 2167-8359

Aprahamian, Mary and Higham, Desmond J. and Higham, Nicholas J. (2016) Matching Exponential-Based and Resolvent-Based Centrality Measures. Journal of Complex Networks, 4 (2). pp. 157-176.

Topping, David and Barley, Mark and Bane, Michael and Higham, Nicholas J. and Aumont, Berbard and Dingle, Nicholas and McFiggans, Gordon (2016) UManSysProp V1.0: An Online and Open-Source Facility for Molecular Property Prediction and Atmospheric Aerosol Calculations. Geoscientific Model Development, 9 (2). pp. 899-914.

Higham, Nicholas J. (2015) Making the Princeton Companion to Applied Mathematics. Mathematics Today, 51 (5). pp. 212-214. ISSN 1361-2042

Higham, Nicholas J. and Strabić, Nataša (2015) Anderson Acceleration of the Alternating Projections Method for Computing the Nearest Correlation Matrix. Numerical Algorithms. pp. 1-22. ISSN 1017-1398

Fasi, Massimiliano and Higham, Nicholas J. and Iannazzo, Bruno (2015) An Algorithm for the Matrix Lambert W Function. SIAM Journal on Matrix Analysis and Applications, 36 (2). pp. 669-685. ISSN 1095-7162

Al-Mohy, Awad H. and Higham, Nicholas J. and Relton, Samuel D. (2015) New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously. SIAM J. Sci. Comput., 37 (1). A456-A487. ISSN 1095-7197

Higham, Nicholas J. and Relton, Samuel D. (2014) Estimating the Condition Number of the Frechet Derivative of a Matrix Function. SIAM Journal on Scientific Computing, 36 (6). C617-C634. ISSN 1064-8275

Higham, Nicholas J. (2014) Sylvester's Influence on Applied Mathematics. Mathematics Today, 50 (4). pp. 202-206. ISSN 1361-2042

Higham, Nicholas J. and Relton, Samuel D. (2014) Higher Order Frechet Derivatives of Matrix Functions and the Level-2 Condition Number. SIAM Journal on Matrix Analysis and Applications, 35 (3). pp. 1019-1037. ISSN 1095-7162

Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2014) Covariance Structure Regularization via Entropy Loss Function. Computational Statistics & Data Analysis, 72. pp. 315-327. ISSN 0167-9473

Aprahamian, Mary and Higham, Nicholas J. (2014) The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. SIAM Journal on Matrix Analysis and Applications, 35 (1). pp. 88-109. ISSN 1095-7162

Higham, Nicholas J. and Lin, Lijing (2013) An Improved Schur--Pade Algorithm for Fractional Powers of a Matrix and their Frechet Derivatives. SIAM. J. Matrix Anal. & Appl., 34 (3). pp. 1341-1360. ISSN 1095-7162

Nakatsukasa, Yuji and Higham, Nicholas J. (2013) Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD. SIAM J. Sci. Comput., 35 (3). A1325-A1349. ISSN 1095-7197

Deadman, Edvin and Higham, Nicholas J. and Ralha, Rui (2013) Blocked Schur Algorithms for Computing the Matrix Square Root. Lecture Notes in Computer Science, 7782. pp. 171-182.

Al-Mohy, Awad H. and Higham, Nicholas J. and Relton, Samuel D. (2013) Computing the Frechet Derivative of the Matrix Logarithm and Estimating the Condition Number. SIAM J. Sci. Comput., 35 (4). C394 -C410. ISSN 1095-7197

Al-Mohy, Awad H. and Higham, Nicholas J. (2012) Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm. SIAM Journal on Scientific Computing, 34 (4). C152-C169. ISSN 1095-7197

Nakatsukasa, Yuji and Higham, Nicholas J. (2012) Backward stability of iterations for computing the polar decomposition. SIAM Journal on Matrix Analysis and Applications, 33 (2). pp. 460-479. ISSN 0895-4798

Nakatsukasa, Yuji and Higham, Nicholas J. (2011) Backward stability of iterations for computing the polar decomposition. SIAM Journal On Matrix Analysis and Applications. ISSN 1749-9097 (In Press)

Bethune, Iain and Bull, J. Mark and Dingle, Nicholas J. and Higham, Nicholas J. (2011) Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations. To appear in International Journal of High Performance Computing Applications. (In Press)

Al-Mohy, Awad H. and Higham, Nicholas J. (2011) Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. SIAM Journal on Scientific Computing, 33 (2). pp. 488-511. ISSN 1064-8275

Grammont, Laurence and Higham, Nicholas J. and Tisseur, Françoise (2011) A Framework for Analyzing Nonlinear Eigenproblems and Parametrized Linear Systems. Linear Algebra and its Applications, 435 (3). pp. 623-640. ISSN 0024-3795

Higham, Nicholas J. (2011) Gaussian Elimination. Wiley Interdisciplinary Reviews: Computational Statistics, 3 (3). pp. 230-238. ISSN 1939-0068

Higham, Nicholas J. and Lin, Lijing (2011) On $p$th Roots of Stochastic Matrices. Linear Algebra and its Applications, 435 (3). pp. 448-463. ISSN 1749-9097

Higham, Nicholas J. and Lin, Lijing (2011) A Schur--Pad\'e Algorithm for Fractional Powers of a Matrix. SIAM J. on Matrix Analysis and Applications, 32 (3). pp. 1056-1078. ISSN 0895-4798

Higham, Nicholas J. and Mehl, Christian and Tisseur, Françoise (2010) The Canonical Generalized Polar Decomposition. SIAM Journal On Matrix Analysis and Applications, 31 (4). 2163 -2180. ISSN 0895-4798

Al-Mohy, Awad H. and Higham, Nicholas J. (2010) The Complex Step Approximation to the Fréchet Derivative of a Matrix Function. Numerical Algorithms, 53 (1). pp. 133-148. ISSN 1017-1398

Higham, Nicholas J. and Al-Mohy, Awad H. (2010) Computing Matrix Functions. Acta Numerica, 19. 159 -208. ISSN 0962-4929

Higham, Nicholas J. and Al-Mohy, Awad H. (2010) Computing Matrix Functions. Acta Numerica, 19. 159 -208. ISSN 0962-4929

Borsdorf, Rüdiger and Higham, Nicholas J. and Raydan, Marcos (2010) Computing a Nearest Correlation Matrix with Factor Structure. SIAM Journal on Matrix Analysis and Applications, 31 (5). pp. 2603-2622. ISSN 1095-7162

Al-Mohy, Awad H. and Higham, Nicholas J. (2009) A New Scaling and Squaring Algorithm for the Matrix Exponential. SIAM Journal On Matrix Analysis and Applications., 31 (3). pp. 970-989. ISSN 1095-7162

Al-Mohy, Awad H. and Higham, Nicholas J. (2009) A New Scaling and Squaring Algorithm for the Matrix Exponential. SIAM Journal On Matrix Analysis and Applications., 31 (3). pp. 970-989. ISSN 1095-7162

Al-Mohy, Awad H. and Higham, Nicholas J. (2009) Computing the Fréchet Derivative of the Matrix Exponential, with an application to Condition Number Estimation. SIAM Journal On Matrix Analysis and Applications., 30 (4). pp. 1639-1657. ISSN 1095-7162

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise (2009) Definite Matrix Polynomials and their Linearization by Definite Pencils. SIAM Journal on Matrix Analysis and Applications, 31 (2). 478 - 502. ISSN 0895-4798

Guo, Chun-Hua and Higham, Nicholas J. and Tisseur, Françoise (2009) Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems. SIAM Journal On Matrix Analysis and Applications., 30 (4). pp. 1593-1613. ISSN 1095-7162

Trefethen, Anne and Higham, Nicholas J. and Duff, Iain and Coveney, Peter (2009) Developing a High-Performance Computing/Numerical Analysis Roadmap. International Journal of High Performance Computing Applications, 23 (4). 423- 426. ISSN 1094-3420

Guo, Chun-Hua and Higham, Nicholas J. and Tisseur, Françoise (2009) An Improved Arc Algorithm for Detecting Definite Hermitian Pairs. SIAM Journal On Matrix Analysis and Applications., 31 (3). 1131- 1151. ISSN 1095-7162

Higham, Nicholas J. (2009) The Scaling and Squaring Method for the Matrix Exponential Revisited. SIAM Review, 51 (4). pp. 747-764. ISSN 0036-1445

Borsdorf, Rudiger and Higham, Nicholas J. (2008) A Preconditioned Newton Algorithm for the Nearest Correlation Matrix. IMA Journal of Numerical Analysis, 30 (1). pp. 94-107. ISSN 1464-3642

Higham, Nicholas J. (2008) Cayley, Sylvester, and Early Matrix Theory. Linear Algebra Appl., 428. pp. 39-43. ISSN 0024-3795

Higham, Nicholas J. (2008) Cayley, Sylvester, and Early Matrix Theory. Linear Algebra Appl., 428. pp. 39-43. ISSN 0024-3795

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise and Garvey, Seamus D. (2008) Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems. International Journal for Numerical Methods in Engineering, 73 (3). pp. 344-360.

Hale, Nicholas and Higham, Nicholas J. and Trefethen, Lloyd N. (2008) Computing $A^\alpha$, $\log(A)$ and Related Matrix Functions by Contour Integrals. SIAM Journal on Numerical Analysis, 46 (5). pp. 2505-2523. ISSN 0036-1429

Higham, Nicholas J. and Li, Ren-Cang and Tisseur, Françoise (2007) Backward Error of Polynomial Eigenproblems Solved by Linearization. SIAM Journal on Matrix Analysis and Applications, 29 (4). pp. 1218-1241. ISSN 0895-4798

Guo, Chun-Hua and Higham, Nicholas J. (2007) Iterative Solution of a Nonsymmetric Algebraic Riccati Equation. SIAM Journal On Matrix Analysis and Applications., 29 (2). pp. 396-412. ISSN 0895-4798

Higham, Nicholas J. (2007) Review of Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators'', by Lloyd N. Trefethen and Mark Embree. Princeton University Press, Princeton, NJ, USA, 2005. Bull. Amer. Math. Soc., 44 (2). pp. 277-284. ISSN 1088-9485

Guo, Chun-Hua and Higham, Nicholas J. (2006) A Schur-Newton Method for the Matrix p'th Root and its Inverse. SIAM Journal On Matrix Analysis and Applications, 28 (3). pp. 788-804. ISSN 0895-4798

Guo, Chun-Hua and Higham, Nicholas J. (2006) A Schur-Newton Method for the Matrix p'th Root and its Inverse. SIAM Journal On Matrix Analysis and Applications, 28 (3). pp. 788-804. ISSN 0895-4798

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise (2006) The Conditioning of Linearizations of Matrix Polynomials. SIAM J. Matrix Anal. Appl., 28 (4). pp. 1005-1028. ISSN 0895-4798

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2006) Symmetric Linearizations for Matrix Polynomials. SIAM Journal on Matrix Analysis and Applications, 29 (1). pp. 143-159. ISSN 0895-4798

Bini, Dario A. and Higham, Nicholas J. and Meini, Beatrice (2005) Algorithms for the Matrix p'th Root. Numerical Algorithms, 39 (4). pp. 349-378. ISSN 1572-9265

Hargreaves, Gareth I. and Higham, Nicholas J. (2005) Efficient Algorithms for the Matrix Cosine and Sine. Numerical Algorithms, 40 (4). pp. 383-400. ISSN 1572-9265

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2005) Functions Preserving Matrix Groups and Iterations for the Matrix Square Root. SIAM Journal On Matrix Analysis and Applications, 26 (3). pp. 849-877. ISSN 1095-7162

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2005) Functions Preserving Matrix Groups and Iterations for the Matrix Square Root. SIAM Journal On Matrix Analysis and Applications, 26 (3). pp. 849-877. ISSN 1095-7162

Higham, Nicholas J. (2005) The Scaling and Squaring Method for the Matrix Exponential Revisited. SIAM Journal On Matrix Analysis and Applications, 26 (4). pp. 1179-1193. ISSN 1095-7162

Higham, Nicholas J. and Konstantinov, Mihail and Mehrmann, Volker and Petkov, Petko (2004) The Sensitivity of Computational Control Problems. IEEE Control Systems Magazine, 24 (1). pp. 28-43. ISSN 0272-1708

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2004) Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups. SIAM Journal On Matrix Analysis and Applications, 25 (4). pp. 1178-1192. ISSN 1095-7162

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2004) Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups. SIAM Journal On Matrix Analysis and Applications, 25 (4). pp. 1178-1192. ISSN 1095-7162

Higham, Nicholas J. (2003) $J$-Orthogonal Matrices: Properties and Generation. SIAM Review, 45 (3). pp. 504-519. ISSN 0036-1445

Davies, Philip I. and Higham, Nicholas J. (2003) A Schur--Parlett Algorithm for Computing Matrix Functions. SIAM Journal On Matrix Analysis and Applications, 25 (2). pp. 464-485. ISSN 1095-7162

Higham, Nicholas J. (2002) Computing the Nearest Correlation Matrix---A Problem from Finance. IMA Journal of Numerical Analysis, 22 (3). pp. 329-343. ISSN 0272-4979

Higham, Nicholas J. and Tisseur, Françoise and Van Dooren, Paul M. (2002) Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Elsevier, Linear Algebra and its Applications, 351-35. pp. 455-474. ISSN 0024-3795

Higham, Nicholas J. and Tisseur, Françoise (2002) More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Elsevier, Linear Algebra and its Applications, 351-35. pp. 435-453. ISSN 0024-3795

Davies, Philip I. and Higham, Nicholas J. and Tisseur, Françoise (2001) Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem. SIAM Journal on Matrix Analysis and Applications, 23 (2). pp. 472-493. ISSN 0895-4798

Tisseur, Françoise and Higham, Nicholas J. (2001) Structured pseudospectra for polynomial eigenvalue problems, with applications. SIAM Journal On Matrix Analysis And Applications, 23 (1). pp. 187-208. ISSN 1095-7162

Davies, Philip I. and Higham, Nicholas J. (2000) Numerically stable generation of correlation matrices and their factors. BIT Numerical Mathematics, 40 (4). pp. 640-651. ISSN 1572-9125

Higham, Nicholas J. (2000) QR factorization with complete pivoting and accurate computation of the SVD. Elsevier, Linear Algebra and its Applications, 309. pp. 153-174. ISSN 0024-3795

Higham, Nicholas J. and Tisseur, Françoise (2000) A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. SIAM Journal On Matrix Analysis And Applications, 21 (4). pp. 1185-1201. ISSN 1095-7162

Cox, Anthony J. and Higham, Nicholas J. (1999) Accuracy and stability of the null space method for solving the equality constrained least squares problem. BIT Numerical Mathematics, 39 (1). pp. 34-50. ISSN 1572-9125

Cox, Anthony J. and Higham, Nicholas J. (1999) Backward error bounds for constrained least squares problems. BIT Numerical Mathematics, 39 (2). pp. 210-227. ISSN 1572-9125

Cox, Anthony J. and Higham, Nicholas J. (1999) Row-wise backward stable elimination methods for the equality constrained least squares problem. SIAM Journal On Matrix Analysis And Applications, 21 (1). pp. 313-326. ISSN 1095-7162

Cheng, Sheung Hun and Higham, Nicholas J. (1999) The nearest definite pair for the Hermitian generalized eigenvalue problem. Linear Algebra and its Applications, 302-30. pp. 63-76. ISSN 0024-3795

Higham, Nicholas J. (1998) Factorizing complex symmetric matrices with positive definite real and imaginary parts. Mathematics of Computation, 67 (224). pp. 1591-1599. ISSN 1088-6842

Higham, Nicholas J. and Cheng, Sheung Hun (1998) Modifying the interia of matrices arising in optimization. Linear Algebra and its Applications, 275-27. pp. 261-279. ISSN 0024-3795

Higham, Desmond J. and Higham, Nicholas J. (1998) Structured backward error and condition of generalized eigenvalue problems. SIAM Journal On Matrix Analysis And Applications, 20 (2). pp. 493-512. ISSN 1095-7162

Cheng, Sheung Hun and Higham, Nicholas J. (1998) A modified Cholesky algorithm based on a symmetric indefinite factorization. SIAM Journal On Matrix Analysis And Applications, 19 (4). pp. 1097-1110. ISSN 1095-7162

Higham, Nicholas J. (1997) Stability of the diagonal pivoting method with partial pivoting. SIAM Journal On Matrix Analysis And Applications, 18 (1). pp. 52-65. ISSN 1095-7162

Higham, Nicholas J. (1997) Stable iterations for the matrix square root. Numerical Algorithms, 15 (2). pp. 227-242. ISSN 1572-9265

Braconnier, Thierry and Higham, Nicholas J. (1996) Computing the field of values and pseudospectra using the Lanczos method with continuation. BIT Numerical Mathematics, 36:3. pp. 422-440. ISSN 1572-9125

Higham, Nicholas J. and Knight, Philip A. (1995) Matrix powers in finite precision arithmetic. SIAM Journal On Matrix Analysis And Applications, 16 (2). pp. 343-358. ISSN 1095-7162

Demmel, James W. and Higham, Nicholas J. and Schreiber, Robert S. (1995) Stability of Block LU Factorization. Numerical Linear Algebra with Applications, Vol. 2 (2). pp. 173-190. ISSN 1070-5325 / 1099-1506

Higham, Nicholas J. (1995) Stability of parallel triangular system solvers. SIAM Journal on Scientific Computing, 16 (2). pp. 400-413. ISSN 1095-7197

Higham, Nicholas J. and Pothen, Alex (1994) Stability of the partitioned inverse method for parallel solution of sparse triangular systems. SIAM Journal on Scientific Computing, 15 (1). pp. 139-148. ISSN 1095-7197

Higham, Nicholas J. (1994) The matrix sign decomposition and its relation to the polar decomposition. Linear Algebra and its Applications, 212-21. pp. 3-20. ISSN 0024-3795

Higham, Nicholas J. and Papadimitriou, Pythagoras (1994) A parallel algorithm for computing the polar decomposition. Elsevier, Parallel Computing, 20. pp. 1161-1173. ISSN 0024-3795

Higham, Nicholas J. and Knight, Philip A. (1993) Finite precision behavior of stationary iteration for solving singular systems. Linear Algebra and its Applications, 192. pp. 165-186. ISSN 0024-3795

Demmel, James W. and Higham, Nicholas J. (1993) Improved error bounds for underdetermined system solvers. SIAM Journal On Matrix Analysis And Applications, 14 (1). pp. 1-14. ISSN 1095-7162

Higham, Nicholas J. (1993) Optimization by direct search in matrix computations. SIAM Journal On Matrix Analysis And Applications, 14 (2). pp. 317-333. ISSN 1095-7162

Higham, Nicholas J. (1993) Perturbation Theory and Backward Error for $AX-XB=C$. BIT Numerical Mathematics, 33. pp. 124-136. ISSN 1572-9125

Higham, Desmond J. and Higham, Nicholas J. (1992) Backward error and condition of structured linear systems. SIAM Journal On Matrix Analysis And Applications, 13 (1). pp. 162-175. ISSN 1095-7162

Higham, Desmond J. and Higham, Nicholas J. (1992) Componentwise perturbation theory for linear systems with multiple right-hand sides. Linear Algebra and its Applications, 174. pp. 111-129. ISSN 0024-3795

Higham, Nicholas J. (1992) Estimating the matrix p-norm. Numerische Mathematik, 62. pp. 539-555. ISSN 0945-3245

Demmel, James W. and Higham, Nicholas J. (1992) Stability of Block Algorithms with Fast Level-3 BLAS. ACM Transactions on Mathematical Software, 18 (3). pp. 274-291. ISSN 0098-3500

Higham, Nicholas J. (1992) Stability of a method for multiplying complex matrices with three real matrix multiplications. SIAM Journal On Matrix Analysis And Applications, 13 (3). pp. 681-687. ISSN 1095-7162

Higham, Nicholas J. (1991) Algorithm 694: A Collection of Test Matrices in MATLAB. ACM Transactions on Mathematical Software, 17 (3). pp. 289-305. ISSN 0098-3500

Higham, Nicholas J. (1991) Iterative refinement enhances the stability of QR factorization methods for solving linear equations. BIT Numerical Mathematics, 31. pp. 447-468. ISSN 1572-9125

Higham, Nicholas J. (1990) Bounding the error in Gaussian elimination for tridiagonal systems. SIAM Journal On Matrix Analysis And Applications, 11 (4). pp. 521-530. ISSN 1095-7162

Higham, Nicholas J. (1990) Experience with a Matrix Norm Estimator. SIAM Journal on Scientific and Statistical Computing, 11 (4). pp. 804-809. ISSN 1095-7197

Higham, Nicholas J. (1990) Exploiting fast matrix multiplication within the level 3 BLAS. ACM Transactions on Mathematical Software, 16 (4). pp. 352-368. ISSN 0098-3500

Higham, Nicholas J. and Schreiber, Robert S. (1990) Fast polar decomposition of an arbitrary matrix. SIAM Journal on Scientific and Statistical Computing, 11 (4). pp. 648-655. ISSN 1095-7197

Higham, Nicholas J. (1990) Stability analysis of algorithms for solving confluent Vandermonde-like systems. SIAM Journal On Matrix Analysis And Applications, 11 (1). pp. 23-41. ISSN 1095-7162

Higham, Nicholas J. and Higham, Desmond J. (1989) Large growth factors in Gaussian elimination with pivoting. SIAM Journal On Matrix Analysis And Applications, 10 (2). pp. 155-164. ISSN 1095-7162

Higham, Nicholas J. (1988) Computing a nearest symmetric positive semidefinite matrix. Linear Algebra and its Applications, 103. pp. 103-118. ISSN 0024-3795

Higham, Nicholas J. (1988) FORTRAN codes for estimating the one-norm of a real or complex matrix, with appliations to condition estimation. ACM Transactions on Mathematical Software, 14 (4). pp. 381-396. ISSN 0098-3500

Higham, Nicholas J. (1988) The symmetric Procrustes problem. BIT Numerical Mathematics, 28. pp. 133-143. ISSN 1572-9125

Higham, Nicholas J. (1987) Computing real square roots of a real matrix. Linear Algebra and its Applications, 88-89. pp. 405-430. ISSN 0024-3795

Higham, Nicholas J. (1987) A Survey of Condition Number Estimation for Triangular Matrices. SIAM Review, 29 (4). pp. 575-596. ISSN 0036-1445

Higham, Nicholas J. (1986) Computing the Polar Decomposition---with Applications. SIAM Journal of Scientific and Statistical Computing, 7 (4). pp. 1160-1174. ISSN 1064-8275

Higham, Nicholas J. (1986) Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix. SIAM Journal of Scientific and Statistical Computing, 7 (1). pp. 150-165. ISSN 1064-8275

Higham, Nicholas J. (1986) Newton's method for the matrix square root. Mathematics of Computation, 46 (174). pp. 537-549. ISSN 00255718

Blanchard, Pierre and Higham, Nicholas J. and Mary, Theo A Class of Fast and Accurate Summation Algorithms. SIAM Journal on Scientific Computing. ISSN 1095-7197 (In Press)

Blanchard, Pierre and Higham, Nicholas J. and Lopez, Florent and Mary, Theo and Pranesh, Srikara Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores. SIAM Journal on Scientific Computing. ISSN 1095-7197 (In Press)

## MIMS Preprint

Fasi, Massimiliano and Higham, Nicholas J. (2020) Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization. [MIMS Preprint]

Higham, Desmond J. and Higham, Nicholas J. and Pranesh, Srikara (2020) Random Matrices Generating Large Growth in LU Factorization with Pivoting. [MIMS Preprint]

Connolly, Michael P. and Higham, Nicholas J. and Mary, Theo (2020) Stochastic Rounding and its Probabilistic Backward Error Analysis. [MIMS Preprint]

Fasi, Massimiliano and Higham, Nicholas J. and Mikaitis, Mantas and Pranesh, Srikara (2020) Numerical Behavior of NVIDIA Tensor Cores. [MIMS Preprint] (Submitted)

Higham, Nicholas J. and Hopkins, Edvin (2020) A Catalogue of Software for Matrix Functions. Version 3.0. [MIMS Preprint]

Fasi, Massimiliano and Higham, Nicholas J. (2020) Generating extreme-scale matrices with specified singular values or condition numbers. [MIMS Preprint]

Carson, Erin and Higham, Nicholas J. and Pranesh, Srikara (2020) Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems. [MIMS Preprint]

Higham, Nicholas J. and Mary, Theo (2020) Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data. [MIMS Preprint] (Submitted)

Blanchard, Pierre and Higham, Desmond J. and Higham, Nicholas J. (2019) Accurately Computing the Log-Sum-Exp and Softmax Functions. [MIMS Preprint]

Higham, Nicholas J. and Mary, Theo (2019) Solving Block Low-Rank Linear Systems by LU Factorization is Numerically Stable. [MIMS Preprint] (Submitted)

Higham, Nicholas J. and Negri Porzio, Gian Maria and Tisseur, Francoise (2019) An Updated Set of Nonlinear Eigenvalue Problems. [MIMS Preprint] (Unpublished)

Higham, Nicholas J. and Pranesh, Srikara (2019) SIMULATING LOW PRECISION FLOATING-POINT ARITHMETIC. [MIMS Preprint]

Higham, Nicholas J. and Pranesh, Srikara and Zounon, Mawussi (2018) Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems. [MIMS Preprint]

Fasi, Massimiliano and Higham, Nicholas J. (2018) An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential. [MIMS Preprint] (In Press)

Higham, Nicholas J. and Mary, Theo (2018) A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error. [MIMS Preprint]

Nadukandi, Prashanth and Higham, Nicholas J. (2018) Computing the Wave-Kernel Matrix Functions. [MIMS Preprint] (Submitted)

Georgescu, Dan I. and Higham, Nicholas J. and Peters, Gareth W. (2017) Explicit Solutions to Correlation Matrix Completion Problems, with an Application to Risk Management and Insurance. [MIMS Preprint]

Anzt, Hartwig and Dongarra, Jack and Flegar, Goran and Higham, Nicholas J. and Quintana-Orti, Enrique S. (2017) Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers. [MIMS Preprint] (In Press)

Carson, Erin and Higham, Nicholas J. (2017) A New Analysis of Iterative Refinement and its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems. [MIMS Preprint]

Higham, Nicholas J. and Kandolf, Peter (2016) Computing the Action of Trigonometric and Hyperbolic Matrix Functions. [MIMS Preprint]

Higham, Nicholas J. and Kandolf, Peter (2016) Computing the Action of Trigonometric and Hyperbolic Matrix Functions. [MIMS Preprint]

Dongarra, Jack and Duff, Iain and Gates, Mark and Haidar, Azzam and Hammarling, Sven and Higham, Nicholas J. and Hogg, Jonathon and Valero-Lara, Pedro and Relton, Samuel D. and Tomov, Stanimire and Zounon, Mawussi (2016) A Proposed API for Batched Basic Linear Algebra Subprograms. [MIMS Preprint]

Aprahamian, Mary and Higham, Nicholas J. (2016) Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms. [MIMS Preprint]

Aprahamian, Mary and Higham, Nicholas J. (2016) Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms. [MIMS Preprint]

Higham, Nicholas J. and Deadman, Edvin (2016) A Catalogue of Software for Matrix Functions. Version 2.0. [MIMS Preprint]

Higham, Nicholas J. and Deadman, Edvin (2016) A Catalogue of Software for Matrix Functions. Version 2.0. [MIMS Preprint]

Higham, Nicholas J. and Deadman, Edvin (2016) A Catalogue of Software for Matrix Functions. Version 2.0. [MIMS Preprint]

Zhang, Weijian and Higham, Nicholas J. (2015) Matrix Depot: An Extensible Test Matrix Collection for Julia. [MIMS Preprint]

Higham, Nicholas J. and Relton, Samuel D. (2015) Estimating the Largest Elements of a Matrix. [MIMS Preprint]

Higham, Nicholas J. and Relton, Samuel D. (2015) Estimating the Largest Elements of a Matrix. [MIMS Preprint]

Higham, Nicholas J. and Strabić, Nataša (2015) Bounds for the Distance to the Nearest Correlation Matrix. [MIMS Preprint]

Higham, Nicholas J. and Strabić, Nataša (2015) Bounds for the Distance to the Nearest Correlation Matrix. [MIMS Preprint]

Higham, Nicholas J. and Strabić, Nataša (2015) Bounds for the Distance to the Nearest Correlation Matrix. [MIMS Preprint]

Higham, Nicholas J. and Strabić, Nataša (2015) Anderson Acceleration of the Alternating Projections Method for Computing the Nearest Correlation Matrix. [MIMS Preprint]

Higham, Nicholas J. and Strabić, Nataša (2015) Anderson Acceleration of the Alternating Projections Method for Computing the Nearest Correlation Matrix. [MIMS Preprint]

Arter, Wayne and Morgan, J. Guy and Relton, Samuel D. and Higham, Nicholas J. (2015) Ranking the Importance of Nuclear Reactions for Activation and Transmutation Events. [MIMS Preprint]

Arter, Wayne and Morgan, J. Guy and Relton, Samuel D. and Higham, Nicholas J. (2015) Ranking the Importance of Nuclear Reactions for Activation and Transmutation Events. [MIMS Preprint]

Aprahamian, Mary and Higham, Desmond J. and Higham, Nicholas J. (2015) Matching Exponential-Based and Resolvent-Based Centrality Measures. [MIMS Preprint]

Aprahamian, Mary and Higham, Desmond J. and Higham, Nicholas J. (2015) Matching Exponential-Based and Resolvent-Based Centrality Measures. [MIMS Preprint]

Aprahamian, Mary and Higham, Desmond J. and Higham, Nicholas J. (2015) Matching Exponential-Based and Resolvent-Based Centrality Measures. [MIMS Preprint]

Fasi, Massimiliano and Higham, Nicholas J. and Iannazzo, Bruno (2014) An Algorithm for the Matrix Lambert W Function. [MIMS Preprint]

Fasi, Massimiliano and Higham, Nicholas J. and Iannazzo, Bruno (2014) An Algorithm for the Matrix Lambert W Function. [MIMS Preprint]

Higham, Nicholas J. and Strabic, Natasa and Sego, Vedran (2014) Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block. [MIMS Preprint]

Higham, Nicholas J. and Strabic, Natasa and Sego, Vedran (2014) Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. and Relton, Samuel D. (2014) New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. and Relton, Samuel D. (2014) New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously. [MIMS Preprint]

Deadman, Edvin and Higham, Nicholas J. (2014) Testing matrix function algorithms using identities. [MIMS Preprint]

Deadman, Edvin and Higham, Nicholas J. (2014) Testing matrix function algorithms using identities. [MIMS Preprint]

Deadman, Edvin and Higham, Nicholas J. (2014) Testing matrix function algorithms using identities. [MIMS Preprint]

Higham, Nicholas J. and Deadman, Edvin (2014) A Catalogue of Software for Matrix Functions. Version 1.0. [MIMS Preprint]

Higham, Nicholas J. and Relton, Samuel D. (2013) Estimating the Condition Number of the Frechet Derivative of a Matrix Function. [MIMS Preprint]

Higham, Nicholas J. and Lijing, Lin (2013) Matrix Functions: A Short Course. [MIMS Preprint]

Higham, Nicholas J. and Relton, Samuel D. (2013) Higher Order Frechet Derivatives of Matrix Functions and the Level-2 Condition Number. [MIMS Preprint]

Higham, Nicholas J. (2013) Matrix Computations in Basic on a Microcomputer. [MIMS Preprint]

Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2013) Covariance Structure Regularization via Entropy Loss Function. [MIMS Preprint]

Kannan, Ramaseshan and Hendry, Stephen and Higham, Nicholas J. and Tisseur, Francoise (2013) Detecting the Causes of Ill-Conditioning in Structural Finite Element Models. [MIMS Preprint]

Aprahamian, Mary and Higham, Nicholas J. (2013) The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. [MIMS Preprint]

Aprahamian, Mary and Higham, Nicholas J. (2013) The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. [MIMS Preprint]

Aprahamian, Mary and Higham, Nicholas J. (2013) The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. [MIMS Preprint]

Aprahamian, Mary and Higham, Nicholas J. (2013) The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. [MIMS Preprint]

Higham, Nicholas J. and Lin, Lijing (2013) An Improved Schur--Pade Algorithm for Fractional Powers of a Matrix and their Frechet Derivatives. [MIMS Preprint]

Higham, Nicholas J. and Lin, Lijing (2013) An Improved Schur--PadÃ© Algorithm for Fractional Powers of a Matrix and their FrÃ©chet Derivatives. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. and Relton, Samuel D. (2012) Computing the Frechet Derivative of the Matrix Logarithm and Estimating the Condition Number. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. and Relton, Samuel D. (2012) Computing the Frechet Derivative of the Matrix Logarithm and Estimating the Condition Number. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. and Relton, Samuel D. (2012) Computing the Frechet Derivative of the Matrix Logarithm and Estimating the Condition Number. [MIMS Preprint]

Bethune, Iain and Bull, J. Mark and Dingle, Nicholas J. and Higham, Nicholas J. (2012) Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP. [MIMS Preprint]

Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2012) Covariance Structure Regularization via Entropy Loss Function. [MIMS Preprint]

Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2012) Covariance Structure Regularization via Entropy Loss Function. [MIMS Preprint]

Nakatsukasa, Yuji and Higham, Nicholas J. (2012) Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD. [MIMS Preprint]

Deadman, Edvin and Higham, Nicholas J. and Ralha, Rui (2012) Blocked Schur Algorithms for Computing the Matrix Square Root. [MIMS Preprint]

Deadman, Edvin and Higham, Nicholas J. and Ralha, Rui (2012) A Recursive Blocked Schur Algorithm for Computing the Matrix Square Root. [MIMS Preprint]

Betcke, Timo and Higham, Nicholas J. and Mehrmann, Volker and Schröder, Christian and Tisseur, Françoise (2011) NLEVP: A Collection of Nonlinear Eigenvalue Problems. [MIMS Preprint]

Betcke, Timo and Higham, Nicholas J. and Mehrmann, Volker and Negri Porzio, Gian Maria and Schröder, Christian and Tisseur, Françoise (2011) NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide. [MIMS Preprint]

Nakatsukasa, Yuji and Higham, Nicholas J. (2011) Backward stability of iterations for computing the polar decomposition. [MIMS Preprint]

Dingle, Nicholas J. and Higham, Nicholas J. (2011) Reducing the Influence of Tiny Normwise Relative Errors on Performance Profiles. [MIMS Preprint]

Dingle, Nicholas J. and Higham, Nicholas J. (2011) Reducing the Influence of Tiny Normwise Relative Errors on Performance Profiles. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2011) Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2011) Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm. [MIMS Preprint]

Bethune, Iain and Bull, J. Mark and Dingle, Nicholas J. and Higham, Nicholas J. (2011) Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations. [MIMS Preprint]

Bethune, Iain and Bull, J. Mark and Dingle, Nicholas J. and Higham, Nicholas J. (2011) Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations. [MIMS Preprint]

Betcke, Timo and Higham, Nicholas J. and Mehrmann, Volker and Schröder, Christian and Tisseur, Françoise (2010) NLEVP: A Collection of Nonlinear Eigenvalue Problems. [MIMS Preprint]

Betcke, Timo and Higham, Nicholas J. and Mehrmann, Volker and Schröder, Christian and Tisseur, Françoise (2010) NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide. [MIMS Preprint]

Higham, Nicholas J. and Lin, Lijing (2010) A Schur--Pad\'e Algorithm for Fractional Powers of a Matrix. [MIMS Preprint]

Higham, Nicholas J. and Lin, Lijing (2010) A Schur--Pad\'e Algorithm for Fractional Powers of a Matrix. [MIMS Preprint]

Higham, Nicholas J. and Lin, Lijing (2010) A Schur--Pad\'e Algorithm for Fractional Powers of a Matrix. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2010) Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2010) Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. [MIMS Preprint]

Borsdorf, Rüdiger and Higham, Nicholas J. and Raydan, Marcos (2009) Computing a Nearest Correlation Matrix with Factor Structure. [MIMS Preprint]

Borsdorf, Rüdiger and Higham, Nicholas J. and Raydan, Marcos (2009) Computing a Nearest Correlation Matrix with Factor Structure. [MIMS Preprint]

Higham, Nicholas J. and Mehl, Christian and Tisseur, Françoise (2009) The Canonical Generalized Polar Decomposition. [MIMS Preprint]

Higham, Nicholas J. and Mehl, Christian and Tisseur, Françoise (2009) The Canonical Generalized Polar Decomposition. [MIMS Preprint]

Grammont, Laurence and Higham, Nicholas J. and Tisseur, Françoise (2009) A Framework for Analyzing Nonlinear Eigenproblems and Parametrized Linear Systems. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2009) The Complex Step Approximation to the Fréchet Derivative of a Matrix Function. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2009) The Complex Step Approximation to the Fréchet Derivative of a Matrix Function. [MIMS Preprint]

Higham, Nicholas J. and Lin, Lijing (2009) On $p$th Roots of Stochastic Matrices. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2009) A New Scaling and Squaring Algorithm for the Matrix Exponential. [MIMS Preprint]

Al-Mohy, Awad H. and Higham, Nicholas J. (2009) A New Scaling and Squaring Algorithm for the Matrix Exponential. [MIMS Preprint]

Trefethen, Anne and Higham, Nicholas J. and Duff, Iain and Coveney, Peter (2009) Applications/Algorithms Roadmapping Activity. First Stage Final Report. [MIMS Preprint]

Higham, Nicholas J. (2008) Cholesky Factorization. [MIMS Preprint]

Guo, Chun-Hua and Higham, Nicholas J. and Tisseur, Françoise (2008) An Improved Arc Algorithm for Detecting Definite Hermitian Pairs. [MIMS Preprint]

Guo, Chun-Hua and Higham, Nicholas J. and Tisseur, Françoise (2008) An Improved Arc Algorithm for Detecting Definite Hermitian Pairs. [MIMS Preprint]

Borsdorf, Rudiger and Higham, Nicholas J. (2008) A Preconditioned Newton Algorithm for the Nearest Correlation Matrix. [MIMS Preprint]

Betcke, Timo and Higham, Nicholas J. and Mehrmann, Volker and Schröder, Christian and Tisseur, Françoise (2008) NLEVP: A Collection of Nonlinear Eigenvalue Problems. [MIMS Preprint]

Higham, Nicholas J. (2008) An Interview with Gene Golub. [MIMS Preprint]

Higham, Nicholas J. (2007) Cayley, Sylvester, and Early Matrix Theory. [MIMS Preprint]

Higham, Nicholas J. (2007) Cayley, Sylvester, and Early Matrix Theory. [MIMS Preprint]

Guo, Chun-Hua and Higham, Nicholas J. and Tisseur, Françoise (2007) Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems. [MIMS Preprint]

Guo, Chun-Hua and Higham, Nicholas J. and Tisseur, Françoise (2007) Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems. [MIMS Preprint]

Hale, Nicholas and Higham, Nicholas J. and Trefethen, Lloyd N. (2007) Computing $A^\alpha$, $\log(A)$ and Related Matrix Functions by Contour Integrals. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise (2007) Definite Matrix Polynomials and their Linearization by Definite Pencils. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise (2007) Definite Matrix Polynomials and their Linearization by Definite Pencils. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise (2007) Definite Matrix Polynomials and their Linearization by Definite Pencils. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise (2007) Notes on Hyperbolic Matrix Polynomials and Definite Linearizations. [MIMS Preprint]

Corless, Robert M. and Ding, Hui and Higham, Nicholas J. and Jeffrey, David J. (2007) The Solution of S exp(S) = A is Not Always the Lambert W Function of A. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise and Garvey, Seamus D. (2007) Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems. [MIMS Preprint]

Hammarling, Sven and Higham, Nicholas J. and Lucas, Craig (2007) LAPACK-Style Codes for Pivoted Cholesky and QR Updating. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise and Garvey, Seamus D. (2006) Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems. [MIMS Preprint]

Hammarling, Sven and Higham, Nicholas J. and Lucas, Craig (2006) LAPACK-Style Codes for Pivoted Cholesky and QR Updating. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2006) Symmetric Linearizations for Matrix Polynomials. [MIMS Preprint]

Guo, Chun-Hua and Higham, Nicholas J. (2006) Iterative Solution of a Nonsymmetric Algebraic Riccati Equation. [MIMS Preprint]

Guo, Chun-Hua and Higham, Nicholas J. (2006) A Schur-Newton Method for the Matrix p'th Root and its Inverse. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2006) Symmetric Linearizations for Matrix Polynomials. [MIMS Preprint]

Guo, Chun-Hua and Higham, Nicholas J. (2005) Iterative Solution of a Nonsymmetric Algebraic Riccati Equation. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2005) Symmetric Linearizations for Matrix Polynomials. [MIMS Preprint]

Higham, Nicholas J. and Mackey, D. Steven and Tisseur, Françoise (2005) The Conditioning of Linearizations of Matrix Polynomials. [MIMS Preprint]

Higham, Nicholas J. (2005) Functions of Matrices. [MIMS Preprint]

Higham, Nicholas J. (2005) An Interview with Peter Lancaster. [MIMS Preprint]

## Book Section

Higham, Nicholas J. (2015) How to Read and Understand a Paper. In: The Princeton Companion to Applied Mathematics. Princeton University Press, Princeton, NJ, USA, pp. 903-906. ISBN 978-0-691-15039-0

Higham, Nicholas J. (2015) Color Spaces and Digital Imaging. In: The Princeton Companion to Applied Mathematics. Princeton University Press, Princeton, NJ, USA, pp. 808-813. ISBN 978-0-691-15039-0

Higham, Nicholas J. (2015) Programming Languages: An Applied Mathematics View. In: The Princeton Companion to Applied Mathematics. Princeton University Press, Princeton, NJ, USA, pp. 828-839. ISBN 978-0-691-15039-0

Higham, Nicholas J. (2015) Numerical Linear Algebra and Matrix Analysis. In: The Princeton Companion to Applied Mathematics. Princeton University Press, Princeton, NJ, USA, pp. 263-281. ISBN 978-0-691-15039-0

Higham, Nicholas J. (2015) The Singular Value Decomposition. In: The Princeton Companion to Applied Mathematics. Princeton University Press, Princeton, NJ, USA, pp. 126-127. ISBN 978-0-691-15039-0

Higham, Nicholas J. (2015) Workflow. In: The Princeton Companion to Applied Mathematics. Princeton University Press, Princeton, NJ, USA, pp. 912-916. ISBN 978-0-691-15039-0

Higham, Nicholas J. (2014) Functions of Matrices. In: Handbook of Linear Algebra. CRC Press, Boca Raton, Florida, USA, 17.1-17.5. ISBN 978-1-4665-0728-9

Higham, Nicholas J. (2014) Functions of Matrices. In: Handbook of Linear Algebra. CRC Press, Boca Raton, Florida, USA, 17.1-17.5. ISBN 978-1-4665-0728-9

Higham, Nicholas J. (2014) Numerical Conditioning. In: Walter Gautschi. Selected Works with Commentaries. Birkhauser, New York, pp. 37-40. ISBN 978-1-4614-7033-5

Higham, Nicholas J. (2007) Commentary on Selected Papers by Gene Golub on Matrix Factorizations and Applications. In: Milestones in Matrix Computation: The Selected Works of Gene H. Golub, with Commentaries. Oxford University Press, Oxford, pp. 227-235. ISBN 978-0-19-920681-0

Higham, Nicholas J. (2006) Functions of Matrices. In: Handbook of Linear Algebra. Chapman and Hall/CRC, Boca Raton, FL, USA, 11.1-11.13. ISBN 1-58488-510-6

Davies, Philip I. and Higham, Nicholas J. (2005) Computing $f(A)b$ for Matrix Functions $f$. In: QCD and Numerical Analysis III. Lecture Notes in Computational Science and Engineering, 47 . Springer-Verlag, Berlin, pp. 15-24. ISBN 3-540-21257-4

Higham, Nicholas J. (1997) Recent Developments in Dense Numerical Linear Algebra. In: The State of the Art in Numerical Analysis. Oxford University Press, Oxford, UK, pp. 1-26. ISBN 0-19-850014-9

Higham, Nicholas J. (1994) A Survey of Componentwise Perturbation Theory. In: Mathematics of Computation 1943--1993: A Half Century of Computational Mathematics. Proceedings of Symposia in Applied Mathematics, 48 . American Mathematical Society, Providence, RI, USA, pp. 49-77. ISBN 0-8218-0291-7

Higham, Nicholas J. (1990) Analysis of the Cholesky Decomposition of a Semi-definite Matrix. In: Reliable Numerical Computation. Oxford University Press, Oxford, UK, pp. 161-185. ISBN 0-19-853564-3

Higham, Nicholas J. (1990) Analysis of the Cholesky Decomposition of a Semi-definite Matrix. In: Reliable Numerical Computation. Oxford University Press, Oxford, UK, pp. 161-185. ISBN 0-19-853564-3

Higham, Nicholas J. and Stewart, G. W. (1987) Numerical Linear Algebra in Statistical Computing. In: The State of the Art in Numerical Analysis. Oxford University Press, Oxford, UK, pp. 41-57. ISBN 0-19-853614-3

## Conference or Workshop Item

Corless, Robert M. and Ding, Hui and Higham, Nicholas J. and Jeffrey, David J. (2007) The Solution of S exp(S) = A is Not Always the Lambert W Function of A. In: ISSAC '07: Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, July 29 - August 01, 2007, Waterloo, Ontario, Canada.

Haidar, Azzam and Tomov, Stanimire and Dongarra, Jack and Higham, Nicholas J. Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers. In: International Conference on Supercomputing, New York, NY, USA, 2018. (In Press)

## Book

Higham, Nicholas J. (2008) Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA. ISBN 978-0-898716-46-7

Higham, Nicholas J. (2002) Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA. ISBN 0-89871-521-0

## Thesis

Higham, Nicholas J. (1985) Nearness Problems in Numerical Linear Algebra. Doctoral thesis, The University of Manchester.

Higham, Nicholas J. (1983) Matrix Condition Numbers. Masters thesis, The University of Manchester.

This list was generated on Mon Aug 3 01:00:48 2020 BST.