On accuracy properties of one-sided bidiagonalization algorithm and its applications

The singular value decomposition (SVD) of a general matrix is the fundamental theoretical and computational tool in numerical linear algebra. The most efficient way to compute the SVD is to reduce the matrix to bidiagonal form in a finite number of orthogonal (unitary) transformations, and then to compute the bidiagonal SVD. This paper gives detailed error analysis and proposes modifications of recently proposed one-sided bidiagonalization procedure, suitable for parallel computing. It also demonstrates its application in solving two common problems in linear algebra.