Name
Title | ||
|---|---|---|
Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices. |
Abstract | ||
|---|---|---|
A real square matrix is said to be totally nonpositive if all of its minors are nonpositive. In this paper, strong relative perturbation bounds are developed for eigenvalues and singular values of totally nonpositive matrices. We first show that there exist exactly n(2) independent variables that parameterize the set of nonsingular totally nonpositive matrices of size n x n. We then show that if such a matrix is perturbed in such a way that each of these parameters has a relative error bounded by is an element of which is small enough, then all the eigenvalues and singular values have small relative errors of order O(n(3)is an element of), with the constant involved in the big-O independent of n, and therefore, these errors are independent of any conventional condition number and increase polynomially with the size of the problem. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140995702 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
totally nonpositive matrices,relative perturbation theory,eigenvalue,singular value,accuracy | Condition number,Combinatorics,Singular value,Perturbation theory,Mathematical analysis,Matrix (mathematics),Square matrix,Invertible matrix,Mathematics,Eigenvalues and eigenvectors,Bounded function | Journal |
Volume | Issue | ISSN |
36 | 2 | 0895-4798 |
Citations | PageRank | References |
3 | 0.41 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rong Huang | 1 | 4 | 1.47 |
| Delin Chu | 2 | 24 | 2.72 |