Journal ArticleDOI
Perturbation bounds for discrete Tikhonov regularisation
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In this article, the authors used the generalised SVD to derive perturbation bounds for the regularised solution when both the matrix and the right-hand side are perturbed.Abstract:
A highly regarded method for solving discrete ill-posed problems is the regularisation method due to Tikhonov (1963) The author uses the generalised SVD to derive perturbation bounds for the regularised solution when both the matrix and the right-hand side are perturbedread more
Citations
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Journal ArticleDOI
Analysis of discrete ill-posed problems by means of the L-curve
TL;DR: The main purpose of this paper is to advocate the use of the graph associated with Tikhonov regularization in the numerical treatment of discrete ill-posed problems, and to demonstrate several important relations between regularized solutions and the graph.
Journal ArticleDOI
REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems
TL;DR: The package REGULARIZATION TOOLS consists of 54 Matlab routines for analysis and solution of discrete ill-posed problems, i.e., systems of linear equations whose coefficient matrix has the properties that its condition number is very large, and its singular values decay gradually to zero.
Journal ArticleDOI
The discrete picard condition of discrete ill-posed problems
TL;DR: In this article, a necessary condition for obtaining good regularized solutions is that the Fourier coefficients of the right-hand side, when expressed in terms of the generalized SVD associated with the regularization problem, on the average decay to zero faster than the generalized singular values.
Journal ArticleDOI
Tikhonov Regularization and Randomized GSVD
TL;DR: A regularization method, combining Tikhonov regularization in general form with the truncated GSVD is proposed, which can achieve good accuracy with less computational time and memory requirement than the classical regularization methods.
References
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Book
Methods for Solving Incorrectly Posed Problems
TL;DR: A new book enPDFd methods for solving incorrectly posed problems that can be a new way to explore the knowledge and get one thing to always remember in every reading time, even step by step is shown.
Journal ArticleDOI
What are the proper condition numbers of discretized III-posed problems?
TL;DR: In this article, the accuracy of approximate solutions of ill-posed equations is discussed, and a discussion of the error of approximated solutions of these problems is presented. But the accuracy is not discussed.