New Fast and Accurate Jacobi SVD Algorithm. II

This paper presents a new one-sided Jacobi SVD algorithm for triangular matrices computed by revealing QR factorizations. If used in the preconditioned Jacobi SVD algorithm, described in part one of this paper, it delivers superior performance leading to the currently fastest method for computing SV...

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Published in:SIAM journal on matrix analysis and applications Vol. 29; no. 4; pp. 1343 - 1362
Main Authors: DRMAC, Zlatko, VESELIC, Kresimir
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2008
Subjects:
Algebra
Algorithms
Applied mathematics
Decomposition
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Nonlinear algebraic and transcendental equations
Norms
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Perturbation theory
Arithmetics
Jacobi method
Decomposition method
Eigenvalue
Implementation
15A18
Numerical analysis
Efficiency
15A12
15A23
65F22
eigenvalues; 15A09
Linear algebra
QR factorization
Floating point
65F15
Matrices
65F35
Fast algorithm
Performance
Computing method
Preconditioning
Singular value decomposition
ISSN:0895-4798, 1095-7162
Online Access:Get full text
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Abstract This paper presents a new one-sided Jacobi SVD algorithm for triangular matrices computed by revealing QR factorizations. If used in the preconditioned Jacobi SVD algorithm, described in part one of this paper, it delivers superior performance leading to the currently fastest method for computing SVD decomposition with high relative accuracy. Furthermore, the efficiency of the new algorithm is comparable to the less accurate bidiagonalization-based methods. The paper also discusses underflow issues in floating point implementation and shows how to use perturbation theory to fix the imperfectness of the machine arithmetic.
AbstractList This paper presents a new one-sided Jacobi SVD algorithm for triangular matrices computed by revealing QR factorizations. If used in the preconditioned Jacobi SVD algorithm, described in part one of this paper, it delivers superior performance leading to the currently fastest method for computing SVD decomposition with high relative accuracy. Furthermore, the efficiency of the new algorithm is comparable to the less accurate bidiagonalization-based methods. The paper also discusses underflow issues in floating point implementation and shows how to use perturbation theory to fix the imperfectness of the machine arithmetic.
Author Drmač, Zlatko
Veselić, Krešimir
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  organization: Department of Mathematics, University of Zagreb, BijeniČka 30, 10000 Zagreb, Croatia
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  givenname: Kresimir
  surname: VESELIC
  fullname: VESELIC, Kresimir
  organization: Lehrgebiet Mathematische Physik, Fernuniversität Hagen, Postfach 940, 58084 Hagen, Germany
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Issue 4
Keywords Perturbation theory
Arithmetics
Jacobi method
Decomposition method
Eigenvalue
Implementation
15A18
Numerical analysis
Efficiency
15A12
15A23
65F22
eigenvalues; 15A09
Linear algebra
QR factorization
Floating point
65F15
Matrices
65F35
Fast algorithm
Performance
Computing method
Preconditioning
Singular value decomposition
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Snippet This paper presents a new one-sided Jacobi SVD algorithm for triangular matrices computed by revealing QR factorizations. If used in the preconditioned Jacobi...
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SubjectTerms Algebra
Algorithms
Applied mathematics
Decomposition
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Nonlinear algebraic and transcendental equations
Norms
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Title New Fast and Accurate Jacobi SVD Algorithm. II
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Volume 29
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