Name
Title | ||
|---|---|---|
A finite-step construction of totally nonnegative matrices with specified eigenvalues |
Abstract | ||
|---|---|---|
Matrices where all minors are nonnegative are said to be totally nonnegative (TN) matrices. In the case of banded TN matrices, which can be expressed by products of several bidiagonal TN matrices, Fukuda et al. (Annal. Mat. Pura Appl. , 423–445, ) discussed the eigenvalue problem from the viewpoint of the discrete hungry Toda (dhToda) equation. The dhToda equation is a discrete integrable system associated with box and ball systems. In this paper, we consider an inverse eigenvalue problem for such banded TN matrices by examining the properties of the dhToda equation. This problem is a real-valued nonnegative inverse eigenvalue problem. First, we show the determinant solution to the dhToda equation with suitable boundary conditions. Next, we clarify the relationship between the characteristic polynomials of the banded TN matrices and the determinant solution. Finally, taking this relationship into account, we design a finite-step procedure for constructing banded TN matrices with specified eigenvalues. We also present an example to demonstrate this procedure. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s11075-015-9957-x | Numerical Algorithms |
Keywords | Field | DocType |
Finite-step construction,Totally nonnegative,Inverse eigenvalue problem,Discrete hungry Toda equation,65F18,15A48,37N30 | Integrable system,Inverse,Boundary value problem,Mathematical optimization,Polynomial,Mathematical analysis,Matrix (mathematics),Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
70 | 3 | 1017-1398 |
Citations | PageRank | References |
1 | 0.41 | 2 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kanae Akaiwa | 1 | 1 | 0.75 |
| Yoshimasa Nakamura | 2 | 48 | 17.38 |
| Masashi Iwasaki | 3 | 27 | 9.42 |
| Hisayoshi Tsutsumi | 4 | 1 | 0.41 |
| koichi | 5 | 6 | 4.18 |