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A Jacobi–Davidson type SVD method. (English) Zbl 1002.65048

Author’s summary: 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 equation. We give a few variants of this Jacobi-Davison singular value decomposition (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.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
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