LAPACK-Style Codes for Pivoted Cholesky and QR Updating

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

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Abstract

Routines exist in LAPACK for computing the Cholesky factorization of a symmetric positive definite matrix and in LINPACK there is a pivoted routine for positive semidefinite matrices. We present new higher level BLAS LAPACK-style codes for computing this pivoted factorization. We show that these can be many times faster than the LINPACK code. Also, with a new stopping criterion, there is more reliable rank detection and smaller normwise backward error. We also present algorithms that update the QR factorization of a matrix after it has had a block of rows or columns added or a block of columns deleted. This is achieved by updating the factors Q and R of the original matrix. We present some LAPACK-style codes and show these can be much faster than computing the factorization from scratch.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Cholesky factorization, QR factorization, complete pivoting, semidefinte matrices, matrix updating, LAPACK
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
Depositing User:	Dr Craig Lucas
Date Deposited:	11 Jan 2007
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/689

Available Versions of this Item

• LAPACK-Style Codes for Pivoted Cholesky and QR Updating. (deposited 06 Oct 2006)
  • LAPACK-Style Codes for Pivoted Cholesky and QR Updating. (deposited 11 Jan 2007) [Currently Displayed]

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