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Methods for solving underdetermined systems
Author(s) -
Qian Jiang,
Andrew Alan L.,
Chu Delin,
Tan Roger C. E.
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2127
Subject(s) - underdetermined system , invertible matrix , eigenvalues and eigenvectors , mathematics , coefficient matrix , matrix (chemical analysis) , eigendecomposition of a matrix , linear system , system of linear equations , algebra over a field , algorithm , pure mathematics , mathematical analysis , physics , materials science , quantum mechanics , composite material
Summary We compare some alternative methods for computing solutions of underdetermined linear systems, A x = 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.