Deadman, Edvin and Higham, Nicholas J. and Ralha, Rui (2012) Blocked Schur Algorithms for Computing the Matrix Square Root. [MIMS Preprint]
PDF
EdvinDeadmanPARA2012.pdf Download (281kB) 
Abstract
The Schur method for computing a matrix square root reduces the matrix to the Schur triangular form and then computes a square root of the triangular matrix. We show that by using either standard blocking or recursive blocking the computation of the square root of the triangular matrix can be made rich in matrix multiplication. Numerical experiments making appropriate use of level 3 BLAS show significant speedups over the point algorithm, both in the square root phase and in the algorithm as a whole. In parallel implementations, recursive blocking is found to provide better performance than standard blocking when the parallelism comes only from threaded BLAS, but the reverse is true when parallelism is explicitly expressed using OpenMP. The excellent numerical stability of the point algorithm is shown to be preserved by blocking. These results are extended to the real Schur method. Blocking is also shown to be effective for multiplying triangular matrices.
Item Type:  MIMS Preprint 

Additional Information:  To appear in Springer Lecture Notes in Computer Science 
Uncontrolled Keywords:  matrix function square root Schur recursive 
Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis 
Depositing User:  Dr Edvin Deadman 
Date Deposited:  05 Dec 2012 
Last Modified:  08 Nov 2017 18:18 
URI:  https://eprints.maths.manchester.ac.uk/id/eprint/1926 
Available Versions of this Item

A Recursive Blocked Schur Algorithm for Computing the Matrix Square Root. (deposited 30 Jan 2012)
 Blocked Schur Algorithms for Computing the Matrix Square Root. (deposited 05 Dec 2012) [Currently Displayed]
Actions (login required)
View Item 