Abstract
In this paper, we propose a new algorithm for computing SVD, with higher accuracy, of matrices with large condition number and/or multiple singular values and/or nearly multiple singular values. With the help of Newton method, we solve a nonlinear system derived from a singular vector on a plane, and an associated singular value. Choosing normal vector of the plane in orthogonal complement space of subspace spanned by obtained singular vectors, all singular-pairs are sequentially obtained by solving its nonlinear system.
