Numerical methods for the computation of analytic singular value decompositions. (English) Zbl 0809.65034

Mehrmann, Volker; Rath, Werner

ETNA, Electron. Trans. Numer. Anal. 1, 72-88 (1993).

Summary: An analytic singular value decomposition (ASVD) for a path of matrices \(E(t)\) is an analytic path of factorizations \(E(t)= X(t) S(t) Y(t)^ T\), where \(X(t)\) and \(Y(t)\) are orthogonal and \(S(t)\) is diagonal. The diagonal entries of \(S(t)\) are allowed to be either positive or negative and to appear in any order. For an analytic path matrix \(E(t)\) an ASVD exists, but this ASVD is not unique. We present two new numerical methods for the computation of unique ASVD’s. One is based on a completely algebraic approach and the other on one-step methods for ordinary differential equations in combination with projections into the set of orthogonal matrices.

MSC:

65F15

Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

analytic singular value decomposition; analytic path matrix

Software:

LAPACK; EISPACK