Accurate Twisted Factorization of Real Symmetric Tridiagonal Matrices and Its Application to Singular Value Decomposition(Algorithms for Matrix・Eigenvalue Problems and their Applications, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Abstract

A new algorithm for an accurate twisted factorization of real symmetric tridiagonal matrices is presented. Two transformations derived from certain discrete Lotka-Volterra (dLV) systems play a key role. The algorithm is shown to be useful to compute singular vectors of upper bidiagonal matrices. Combining it with the mdLVs algorithm for accurate singular values, a new singular value decomposition (SVD) algorithm named integrable SVD (I-SVD) algorithm is designed. It is shown that I-SVD runs much faster than a credible SVD routine DBDSQR with the same accuracy at least in three different types of test matrices.