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Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill‐posed problems
Author(s) -
Chu Delin,
Lin Lijing,
Tan Roger C. E.,
Wei Yimin
Publication year - 2011
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.702
Subject(s) - tikhonov regularization , mathematics , regularization (linguistics) , backus–gilbert method , condition number , well posed problem , perturbation (astronomy) , regularization perspectives on support vector machines , mathematical analysis , inverse problem , eigenvalues and eigenvectors , computer science , physics , quantum mechanics , artificial intelligence
One of the most successful methods for solving the least‐squares problem min x ∥ Ax − b ∥ 2 with a highly ill‐conditioned or rank deficient coefficient matrix A is the method of Tikhonov regularization. In this paper, we derive the normwise, mixed and componentwise condition numbers and componentwise perturbation bounds for the Tikhonov regularization. Our results are sharper than the known results. Some numerical examples are given to illustrate our results. Copyright © 2010 John Wiley & Sons, Ltd.