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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Hammarling, S., Higham, N. J., & Lucas, C. (2007). LAPACK-style codes for pivoted cholesky and QR updating. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4699 LNCS, pp. 137–146). Springer Verlag. https://doi.org/10.1007/978-3-540-75755-9_17
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