Multifrontal Computation with the Orthogonal Factors of Sparse Matrices (1994)
| Venue: | SIAM Journal on Matrix Analysis and Applications |
| Citations: | 7 - 0 self |
BibTeX
@ARTICLE{Lu94multifrontalcomputation,
author = {Szu-Min Lu and Jesse and Jesse L. Barlow},
title = {Multifrontal Computation with the Orthogonal Factors of Sparse Matrices},
journal = {SIAM Journal on Matrix Analysis and Applications},
year = {1994},
volume = {17}
}
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Abstract
. This paper studies the solution of the linear least squares problem for a large and sparse m by n matrix A with m n by QR factorization of A and transformation of the righthand side vector b to Q T b. A multifrontal-based method for computing Q T b using Householder factorization is presented. A theoretical operation count for the K by K unbordered grid model problem and problems defined on graphs with p n-separators shows that the proposed method requires O(NR ) storage and multiplications to compute Q T b, where NR = O(n log n) is the number of nonzeros of the upper triangular factor R of A. In order to introduce BLAS-2 operations, Schreiber and Van Loan's Storage-Efficient-WY Representation [SIAM J. Sci. Stat. Computing, 10(1989),pp. 55-57] is applied for the orthogonal factor Q i of each frontal matrix F i . If this technique is used, the bound on storage increases to O(n(logn) 2 ). Some numerical results for the grid model problems as well as Harwell-Boeing problems...
