Iterative SVD-based methods for ill-posed problems. [Singular value decomposition]
- Montana State Univ., Bozeman, MT (United States). Dept. of Mathematical Sciences
- 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), Vol. 15:3; ISSN 0196-5204
- Country of Publication:
- United States
- Language:
- English
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