Methods for solving underdetermined systems

Summary We compare some alternative methods for computing solutions of underdetermined linear systems, Ax=b. Each method involves solving an associated system with a different nonsingular coefficient matrix, A˜. We obtain bounds on the condition numbers of these nonsingular matrices and test the met...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2018-01, Vol.25 (1), p.n/a
Main Authors: Qian, Jiang, Andrew, Alan L., Chu, Delin, Tan, Roger C. E.
Format: Article
Language:English
Subjects:
Computation
condition number
derivatives of eigenvectors
Linear systems
Numerical methods
Test procedures
underdetermined linear systems
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Summary:Summary We compare some alternative methods for computing solutions of underdetermined linear systems, Ax=b. Each method involves solving an associated system with a different nonsingular coefficient matrix, A˜. We obtain bounds on the condition numbers of these nonsingular matrices and test the methods on numerical examples. We discuss implications for computing eigenvector derivatives and make some recommendations.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2127