Incremental condition estimation for sparse matrices

Journal Article · Mon Oct 01 00:00:00 EDT 1990 · SIAM Journal on Matrix Analysis and Applications

DOI:https://doi.org/10.1137/0611047· OSTI ID:7206513

Bischof, C. H. ^[1]; Lewis, J. G.; Pierce, D. J. ^[2]

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1. Argonne National Lab., IL (United States)
2. Boeing Computer Servies, Seattle, WA (United States)

Incremental condition estimation provides an estimate for the smallest singular value of a triangular matrix. In particular, it gives a running estimate of the smallest singular value of a triangular factor matrix as the factor is generated one column or row at a time. An incremental condition estimator for dense matrices was originally suggested by Bischof. In this paper this scheme is generalized to handle sparse triangular matrices, especially those that are factors of sparse matrices. Numerical experiments on a variety of matrices demonstrate the reliability of this scheme in estimating the smallest singular value. A partial description of its implementation in a sparse matrix factorization code further illustrates its practicality.

• Sponsoring Organization: USDOE
• OSTI ID: 7206513
• Journal Information: SIAM Journal on Matrix Analysis and Applications, Vol. 11, Issue 4; ISSN 0895-4798
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
MATRICES
NUMERICAL SOLUTION
PARALLEL PROCESSING
ALGORITHMS
OPTIMIZATION
MATHEMATICAL LOGIC
PROGRAMMING
990200* - Mathematics & Computers