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Real Rectangular Matrices

  • Jane K. Cullum
  • Ralph A. Willoughby
Part of the Progress in Scientific Computing book series (PSC, volume 4)

Abstract

The FORTRAN codes in this Chapter address the question of computing distinct singular values and corresponding left and right singular vectors of real rectangular matrices, using a single-vector Lanczos procedure. For a given real rectangular ℓ × n matrix A, these codes compute nonnegative scalars σ and corresponding real vectors x ≠ 0 and y ≠ 0 such that
(6.1.1)
Every real rectangular ℓxn matrix, where ℓ n, has a singular value decomposition,
(6.1.2)
where Σ is ℓ × n and = diag {σ1,..., σn} with σi, 1 ≤ i ≤ n, the singular values of A. X is a n × n orthogonal matrix, Y is a ℓ × ℓ orthogonal matrix, and the columns of X and of Y are respectively, right and left singular vectors of A. There are many applications for this type of decomposition. Singular values and vectors are discussed in detail for example in Stewart [1973].

Keywords

Error Estimate Singular Vector Main Program Vector Computation Real Symmetric Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, Inc. 1985

Authors and Affiliations

  • Jane K. Cullum
    • 1
  • Ralph A. Willoughby
    • 1
  1. 1.IBM T. J. Watson Research CenterYorktown HeightsUSA

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