Generalized Golub--Kahan Bidiagonalization and Stopping Criteria
نویسندگان
چکیده
منابع مشابه
Generalized Golub-Kahan Bidiagonalization and Stopping Criteria
The Golub–Kahan bidiagonalization algorithm has been widely used in solving leastsquares problems and in the computation of the SVD of rectangular matrices. Here we propose an algorithm based on the Golub–Kahan process for the solution of augmented systems that minimizes the norm of the error and, in particular, we propose a novel estimator of the error similar to the one proposed by Hestenes a...
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The concept of the core problem in total least squares (TLS) problems was introduced in [C. C. Paige and Z. Strakoš, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861–875]. It is based on orthogonal transformations such that the resulting problem decomposes into two independent parts, with one of the parts having trivial (zero) right-hand side and maximal dimensions, and the other part with nonzero...
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We consider the solution of large linear systems of equations that arise from the discretization of ill-posed problems. The matrix has a Kronecker product structure and the right-hand side is contaminated by measurement error. Problems of this kind arise, for instance, from the discretization of Fredholm integral equations of the first kind in two space-dimensions with a separable kernel and in...
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In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...
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Generalized Cross Validation (GCV) is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small-scale problems, but prohibitively expensive to compute for large-scale ones. This paper describes a novel method, based on Gauss-type quadrature, for determining up...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2013
ISSN: 0895-4798,1095-7162
DOI: 10.1137/120866543