Multifrontal computation with the orthogonal factors of sparse matrices

Szu Min Lu, Jesse L. Barlow

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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 right-hand side vector 6 to QTb. A multifrontal-based method for computing QTb using Householder factorization is presented. A theoretical operation count for the K by K unbordered grid model problem and problems defined on graphs with √n-separators shows that the proposed method requires O(NR) storage and multiplications to compute QTb, 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. Comput., 10 (1989), pp. 53-57] is applied for the orthogonal factor Qi of each frontal matrix Fi. If this technique is used, the bound on storage increases to O(n(log n)2). Some numerical results for the grid model problems as well as Harwell-Boeing problems are provided.

Original languageEnglish (US)
Pages (from-to)658-679
Number of pages22
JournalSIAM Journal on Matrix Analysis and Applications
Volume17
Issue number3
DOIs
Publication statusPublished - Jul 1996

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All Science Journal Classification (ASJC) codes

  • Analysis

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