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Square regularization matrices for large linear discrete ill‐posed problems
Author(s) -
Donatelli Marco,
Neuman Arthur,
Reichel Lothar
Publication year - 2012
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.1833
Subject(s) - tikhonov regularization , backus–gilbert method , regularization (linguistics) , mathematics , well posed problem , regularization perspectives on support vector machines , inverse problem , mathematical optimization , mathematical analysis , computer science , artificial intelligence
SUMMARY Large linear discrete ill‐posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods based on the Arnoldi process for large‐scale Tikhonov regularization problems. Copyright © 2012 John Wiley & Sons, Ltd.