Computing Singular Value Decompositions of Parameterized Matrices with Total Nonpositivity to High Relative Accuracy

Abstract

In the last years, much effort has been devoted to high relative accuracy algorithms for the singular value problem. However, such algorithms have been constructed only for a few classes of matrices with certain structure or properties. In this paper, we study a different class of matrices--parameterized matrices with total nonpositivity. We develop a new algorithm to compute singular value decompositions of such matrices to high relative accuracy. Our numerical results confirm the high relative accuracy of our algorithm.