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On the computation of a truncated SVD of a large linear discrete ill-posed problem

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    Enyinda Onunwor & Lothar Reichel

  2. Department of Mathematics, Stark State College, 6200 Frank Ave. NW, North Canton, OH, 44720, USA

    Enyinda Onunwor

Authors
  1. Enyinda Onunwor
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  2. Lothar Reichel
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Correspondence to Lothar Reichel.

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Dedicated to Ken Hayami on the occasion of his 60th birthday.

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Onunwor, E., Reichel, L. On the computation of a truncated SVD of a large linear discrete ill-posed problem. Numer Algor 75, 359–380 (2017). https://doi.org/10.1007/s11075-016-0259-8

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  • DOI: https://doi.org/10.1007/s11075-016-0259-8

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