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A unified approach to solving ill‐conditioned matrix problems
Author(s) -
Rothwell E.,
Drachman B.
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620280309
Subject(s) - singular value decomposition , regularization (linguistics) , residual , mathematics , simple (philosophy) , matrix (chemical analysis) , mathematical optimization , condition number , singular value , algorithm , computer science , eigenvalues and eigenvectors , artificial intelligence , philosophy , materials science , physics , epistemology , quantum mechanics , composite material
A unified approach to solving ill‐conditioned matrix problems is presented, concentrating on those problems arising in engineering where measurement inaccuracy is the major source of error. By applying the singular value decomposition, it is shown that regularization with a parameter can be used without squaring the condition number of the matrix. Numerical examples demonstrate that a smaller relative error is attainable using the unified approach over the more standard technique of discarding singular values. Lastly, a simple method is presented for locating the optimal solution using a computed residual.