Abstract

We discuss a new method for the iterative computation of a portion of the singular values and vectors of a large sparse matrix. Similar to the Jacobi--Davidson method for the eigenvalue problem, we compute in each step a correction by (approximately) solving a correction equation. We give a few variants of this Jacobi--Davidson SVD (JDSVD) method with their theoretical properties. It is shown that the JDSVD can be seen as an accelerated (inexact) Newton scheme. We experimentally compare the method with some other iterative SVD methods.

MSC codes

  1. 65F15
  2. 65F35

Keywords

  1. Jacobi--Davidson
  2. singular value decomposition (SVD)
  3. singular values
  4. singular vectors
  5. norm
  6. augmented matrix
  7. correction equation
  8. (inexact) accelerated Newton
  9. improving singular values

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: 606 - 628
ISSN (online): 1095-7197

History

Published online: 4 August 2006

MSC codes

  1. 65F15
  2. 65F35

Keywords

  1. Jacobi--Davidson
  2. singular value decomposition (SVD)
  3. singular values
  4. singular vectors
  5. norm
  6. augmented matrix
  7. correction equation
  8. (inexact) accelerated Newton
  9. improving singular values

Authors

Affiliations

Michiel E. Hochstenbach

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