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

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

LAPACK; EISPACK
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