A finite-step construction of totally nonnegative matrices with specified eigenvalues

被引：3
|
作者：
Akaiwa, Kanae [1 ]
Nakamura, Yoshimasa [1 ]
Iwasaki, Masashi [2 ]
Tsutsumi, Hisayoshi [3 ]
Kondo, Koichi [3 ]
机构：
[1] Kyoto Univ, Grad Sch Informat, Sakyo Ku, Kyoto 6068501, Japan
[2] Kyoto Prefectural Univ, Dept Informat & Environm Sci, Sakyo Ku, Kyoto 6068522, Japan
[3] Doshisha Univ, Grad Sch Sci & Engn, Kyotanabe, Kyoto 6100394, Japan
来源：
NUMERICAL ALGORITHMS | 2015年 / 70卷 / 03期
基金：
日本学术振兴会;
关键词：
Finite-step construction; Totally nonnegative; Inverse eigenvalue problem; Discrete hungry Toda equation; ALGORITHM; SYSTEMS;
D O I：
10.1007/s11075-015-9957-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. 192, 423-445, 2013) 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.
引用
收藏
页码：469 / 484
页数：16
相关论文
共 50 条
  • [1] A finite-step construction of totally nonnegative matrices with specified eigenvalues
    Kanae Akaiwa
    Yoshimasa Nakamura
    Masashi Iwasaki
    Hisayoshi Tsutsumi
    Koichi Kondo
    [J]. Numerical Algorithms, 2015, 70 : 469 - 484
  • [2] An arbitrary band structure construction of totally nonnegative matrices with prescribed eigenvalues
    Kanae Akaiwa
    Yoshimasa Nakamura
    Masashi Iwasaki
    Akira Yoshida
    Koichi Kondo
    [J]. Numerical Algorithms, 2017, 75 : 1079 - 1101
  • [3] An arbitrary band structure construction of totally nonnegative matrices with prescribed eigenvalues
    Akaiwa, Kanae
    Nakamura, Yoshimasa
    Iwasaki, Masashi
    Yoshida, Akira
    Kondo, Koichi
    [J]. NUMERICAL ALGORITHMS, 2017, 75 (04) : 1079 - 1101
  • [4] cAccurate eigenvalues and SVDs of totally nonnegative matrices
    Koev, P
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2005, 27 (01) : 1 - 23
  • [5] REFINEMENTS ON THE INTERLACING OF EIGENVALUES OF CERTAIN TOTALLY NONNEGATIVE MATRICES
    Fallat, Shaun M.
    Woerdeman, Hugo J.
    [J]. OPERATORS AND MATRICES, 2007, 1 (02): : 271 - 281
  • [6] Accurate eigenvalues and exact zero Jordan blocks of totally nonnegative matrices
    Koev, Plamen
    [J]. NUMERISCHE MATHEMATIK, 2019, 141 (03) : 693 - 713
  • [7] Accurate eigenvalues and exact zero Jordan blocks of totally nonnegative matrices
    Plamen Koev
    [J]. Numerische Mathematik, 2019, 141 : 693 - 713
  • [8] Eigenvalues of nonnegative matrices
    Guo, WW
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 266 : 261 - 270
  • [9] TOTALLY NONNEGATIVE MOMENT MATRICES
    HEILIGERS, B
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1994, 199 : 213 - 227
  • [10] Intervals of totally nonnegative matrices
    Adm, Mohammad
    Garloff, Juergen
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 439 (12) : 3796 - 3806
12345