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Numerical Linear Algebra with Applications by William Ford

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Chapter 23

Computing the Singular Value Decomposition

Abstract

This chapter develops two algorithms for the computation of the SVD. The first of these is the one-sided Jacobi method. By properly choosing c and s, right Jacobi rotations can be constructed that reduce A to a diagonal matrix of singular values. The result is the same if AT*A is reduced to the matrix of singular values using orthogonality transformations. This algorithm is particularly effective when computing small singular values. The computation of singular values is well conditioned, but the computation of left and right singular vectors can be ill-conditioned if some singular values are close together. There is a variant of the one-sided Jacobi algorithm that provides higher ...

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