Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems

One of the most successful methods for solving the least‐squares problem minx∥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 pertu...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2011-01, Vol.18 (1), p.87-103
Main Authors: Chu, Delin, Lin, Lijing, Tan, Roger C. E., Wei, Yimin
Format: Article
Language:English
Subjects:
Coefficients
condition number
Ill posed problems
Least squares method
Linear algebra
linear least squares
Mathematical models
perturbation
Perturbation methods
Regularization
Tikhonov regularization
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Summary:One of the most successful methods for solving the least‐squares problem minx∥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.
ISSN:1070-5325
1099-1506
1099-1506
DOI:10.1002/nla.702