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2006.385: LAPACK-Style Codes for Pivoted Cholesky and QR Updating

2006.385: Sven Hammarling, Nicholas J. Higham and Craig Lucas (2007) LAPACK-Style Codes for Pivoted Cholesky and QR Updating.

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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 2000 > 15 Linear and multilinear algebra; matrix theory
MIMS number:2006.385
Deposited By:Dr Craig Lucas
Deposited On:11 January 2007

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