Some matrix nearness problems suggested by Tikhonov regularization
نویسندگان
چکیده
منابع مشابه
Matrix Nearness Problems and Applications ∗
A matrix nearness problem consists of finding, for an arbitrary matrix A, a nearest member of some given class of matrices, where distance is measured in a matrix norm. A survey of nearness problems is given, with particular emphasis on the fundamental properties of symmetry, positive definiteness, orthogonality, normality, rank-deficiency and instability. Theoretical results and computational ...
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Tikhonov regularization is a powerful tool for the solution of ill-posed linear systems and linear least squares problems. The choice of the regularization parameter is a crucial step, and many methods have been proposed for this purpose. However, eecient and reliable methods for large scale problems are still missing. In this paper approximation techniques based on the Lanczos algorithm and th...
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Many popular solution methods for large discrete ill-posed problems are based on Tikhonov regularization and compute a partial Lanczos bidiagonalization of the matrix. The computational effort required by these methods is not reduced significantly when the matrix of the discrete ill-posed problem, rather than being a general nonsymmetric matrix, is symmetric and possibly indefinite. This paper ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.04.008