A sparse counterpart of Reichel and Gragg’s package QRUP |
| |
Authors: | Pablo Guerrero-García Ángel Santos-Palomo |
| |
Institution: | Department of Applied Mathematics, University of Málaga, 29071 Málaga, Spain |
| |
Abstract: | We describe how to maintain the triangular factor of a sparse QR factorization when columns are added and deleted and Q cannot be stored for sparsity reasons. The updating procedures could be thought of as a sparse counterpart of Reichel and Gragg’s package QRUP. They allow us to solve a sequence of sparse linear least squares subproblems in which each matrix Bk is an independent subset of the columns of a fixed matrix A, and Bk+1 is obtained by adding or deleting one column. Like Coleman and Hulbert T. Coleman, L. Hulbert, A direct active set algorithm for large sparse quadratic programs with simple bounds, Math. Program. 45 (1989) 373-406], we adapt the sparse direct methodology of Björck and Oreborn of the late 1980s, but without forming ATA, which may be only positive semidefinite. Our Matlab 5 implementation works with a suitable row and column numbering within a static triangular sparsity pattern that is computed in advance by symbolic factorization of ATA and preserved with placeholders. |
| |
Keywords: | 65F50 65F20 |
本文献已被 ScienceDirect 等数据库收录! |
|