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2001•SIAM Journal on Scientific ComputingOpen access

A Jacobi--Davidson Type SVD Method

Michiel E. Hochstenbach

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Abstract

We discuss a new method for the iterative computation of a portion of the singular values and vectors of a large sparse matrix. Similar to the Jacobi--Davidson method for the eigenvalue problem, we compute in each step a correction by (approximately) solving a correction equation. We give a few variants of this Jacobi--Davidson SVD (JDSVD) method with their theoretical properties. It is shown that the JDSVD can be seen as an accelerated (inexact) Newton scheme. We experimentally compare the method with some other iterative SVD methods.

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What this paper is about

We discuss a new method for the iterative computation of a portion of the singular values and vectors of a large sparse matrix. Similar to the Jacobi--Davidson method for the eigenvalue problem, we compute in each step a correction by (approximately) solving a correction equation. We give a few variants of this Jacobi--Davidson SVD (JDSVD) method with their theoretical properties. It is shown that the JDSVD can be seen as an accelerated (inexact) Newton scheme. We experimentally compare the method with some other iterative SVD methods.

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Available abstract

We discuss a new method for the iterative computation of a portion of the singular values and vectors of a large sparse matrix. Similar to the Jacobi--Davidson method for the eigenvalue problem, we compute in each step a correction by (approximately) solving a correction equation. We give a few variants of this Jacobi--Davidson SVD (JDSVD) method with their theoretical properties. It is shown that the JDSVD can be seen as an accelerated (inexact) Newton scheme. We experimentally compare the method with some other iterative SVD methods.

Key concepts: Singular value decomposition, Mathematics, Jacobi method, Eigenvalues and eigenvectors, Computation, Iterative method, Singular value, Applied mathematics

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