Prestructuring sparse matrices with dense rows and columns via null space methods

Summary Several applied problems may produce large sparse matrices with a small number of dense rows and/or columns, which can adversely affect the performance of commonly used direct solvers. By posing the problem as a saddle point system, an unconventional application of a null space method can be...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2018-03, Vol.25 (2), p.n/a
Main Author: Howell, Jason S.
Format: Article
Language:English
Subjects:
dense column
dense row
direct method
null space method
prestructuring
saddle point problem
Saddle points
Solvers
Sparse matrices
Sparsity
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Summary:Summary Several applied problems may produce large sparse matrices with a small number of dense rows and/or columns, which can adversely affect the performance of commonly used direct solvers. By posing the problem as a saddle point system, an unconventional application of a null space method can be employed to eliminate dense rows and columns. The choice of null space basis is critical in retaining the overall sparse structure of the matrix. A new one‐sided application of the null space method is also presented to eliminate either dense rows or columns. These methods can be considered techniques that modify the nonzero structure of the matrix before employing a direct solver and may result in improved direct solver performance.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2133