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
Every real rectangular ℓxn matrix, where ℓ ≥ n, has a singular value decomposition,
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].
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© 1985 Birkhäuser Boston, Inc.
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Cullum, J.K., Willoughby, R.A. (1985). Real Rectangular Matrices. In: Lanczos Algorithms for Large Symmetric Eigenvalue Computations Vol. II Programs. Progress in Scientific Computing, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-9178-4_6
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DOI: https://doi.org/10.1007/978-1-4684-9178-4_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-9180-7
Online ISBN: 978-1-4684-9178-4
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