On the computation of a truncated SVD of a large linear discrete ill-posed problem |
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Authors: | Enyinda Onunwor Lothar Reichel |
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Affiliation: | 1.Department of Mathematical Sciences,Kent State University,Kent,USA;2.Department of Mathematics,Stark State College,North Canton,USA |
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Abstract: | The singular value decomposition is commonly used to solve linear discrete ill-posed problems of small to moderate size. This decomposition not only can be applied to determine an approximate solution but also provides insight into properties of the problem. However, large-scale problems generally are not solved with the aid of the singular value decomposition, because its computation is considered too expensive. This paper shows that a truncated singular value decomposition, made up of a few of the largest singular values and associated right and left singular vectors, of the matrix of a large-scale linear discrete ill-posed problems can be computed quite inexpensively by an implicitly restarted Golub–Kahan bidiagonalization method. Similarly, for large symmetric discrete ill-posed problems a truncated eigendecomposition can be computed inexpensively by an implicitly restarted symmetric Lanczos method. |
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