Verified bounds for all the singular values of matrix

摘要

Algorithms for computing verified bounds of all singular values of matrix are proposed. It is shown that the proposed bounds are equal or tighter than previous bounds. The computational costs of the proposed algorithms are equal or smaller than those of the previous algorithms. Numerical results show the properties of the proposed algorithms. As an application of the proposed algorithms, algorithms for computing verified bounds of all generalized singular values are also sketched.