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.
This is the latest version of this eprint.
Full text available as:
 | PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 126 Kb |
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 |
Available Versions of this Item
- LAPACK-Style Codes for Pivoted Cholesky and QR Updating (deposited 11 January 2007) [Currently Displayed]
Download Statistics: last 4 weeks
Repository Staff Only: edit this item