Iterative SVD-based methods for ill-posed problems. [Singular value decomposition]

Journal Article · Sun May 01 04:00:00 EDT 1994 · SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States)

OSTI ID:7112108

Vogel, C R ^[1]; Wade, J G ^[2]

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1. Montana State Univ., Bozeman, MT (United States). Dept. of Mathematical Sciences
2. Bowling Green State Univ., Bowling Green, OH (United States). Dept. of Mathematics and Statistics

Very large matrices with rapidly decaying singular values commonly arise in the numerical solution of ill-posed problems. The singular value decomposition (SVD) is a basic tool for both the analysis and computation of solutions to such problems. In most applications, it suffices to obtain a partial SVD consisting of only the largest singular values and their corresponding singular vectors. In this paper, two separate approaches -- one based on subspace iteration and the other based on the Lanczos method -- are considered for the efficient iterative computation of partial SVDs. In the context of ill-posed problems, an analytical and numerical comparison of these two methods is made and the role of the regularization operator in convergence acceleration is explored.

• OSTI ID: 7112108
• Journal Information: SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States) Vol. 15:3; ISSN 0196-5204; ISSN SIJCD4
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
CALCULATION METHODS
COMPARATIVE EVALUATIONS
CONVERGENCE
EVALUATION
ITERATIVE METHODS
MATRICES
NUMERICAL SOLUTION
SINGULARITY