کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4640871 | 1341290 | 2010 | 6 صفحه PDF | دانلود رایگان |
We describe how to maintain the triangular factor of a sparse QR factorization when columns are added and deleted and QQ 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 BkBk is an independent subset of the columns of a fixed matrix AA, and Bk+1Bk+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 ATAATA, 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 ATAATA and preserved with placeholders.
Journal: Journal of Computational and Applied Mathematics - Volume 233, Issue 5, 1 January 2010, Pages 1232–1237