Optimal Gerschgorin‐type inclusion intervals of singular values
Hou‐Biao Li, Ting‐Zhu Huang, Hong Li, Shu‐Qian Shen · Numerical Linear Algebra with Applications · 2006
Abstract In this paper, some optimal inclusion intervals of matrix singular values are discussed in the set ΩA of matrices equimodular with matrix A. These intervals can be obtained by extensions of the Gerschgorin‐type theorem for singular values, based only on the use of positive scale vectors and their intersections. Theoretic analysis and numerical examples show that upper bounds of these intervals are optimal in some cases and lower bounds may be non‐trivial (i.e. positive) when PA is a H‐matrix, where P is a permutation matrix, which improves the conjecture in Reference (Linear Algebra Appl 1984; 56:105‐119). Copyright © 2006 John Wiley & Sons, Ltd.