Eigenvalues of Hadamard powers of large symmetric Pascal matrices

被引：2
|
作者：
Ashrafi, A
Gibson, PM
机构：
[1] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA
[2] Univ Alabama, Dept Elect & Comp Engn, Huntsville, AL 35899 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 405卷
关键词：
eigenvalues; symmetric Pascal matrices; real Hadamard powers; Perron roots; positive matrices; positive definite matrices; convergence; MATLAB;
D O I：
10.1016/j.laa.2005.02.041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let S, be the positive real symmetric matrix of order n with (i, j) entry equal to [GRAPHICS] and let x be a positive real number. Eigenvalues of the Hadamard (or entry j - I wise) power S-n((x)) are considered. In particular for k a positive integer, it is shown that both the Perron root and the trace of S-n((k)) are approximately equal to 4(k)/4(k)-1 [GRAPHICS] (C) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：60 / 66
页数：7
相关论文
共 50 条
  • [41] A simple estimate for the smaller eigenvalues of symmetric matrices
    Gonzalez, Augusto
    [J]. REVISTA CUBANA DE FISICA, 2010, 27 (2B): : 208 - 211
  • [42] On eigenvalues of symmetric matrices with PSD principal submatrices
    Kozhasov, Khazhgali
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2023, 119 : 90 - 100
  • [43] Analysis and Computation of Eigenvalues of Symmetric Fuzzy Matrices
    De Vlieger, Jeroen
    Meerbergen, Karl
    [J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2, 2009, 1168 : 278 - 281
  • [44] Asymptotics of eigenvalues of symmetric Toeplitz band matrices
    Batalshchikov, A. A.
    Grudsky, S. M.
    Stukopin, V. A.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 469 : 464 - 486
  • [45] Eigenvalues of symmetric matrices over integral domains
    Kummer, Mario
    [J]. JOURNAL OF ALGEBRA, 2016, 466 : 195 - 203
  • [46] LOCATING EIGENVALUES OF SYMMETRIC MATRICES- A SURVEY*
    Hoppen, Carlos
    Jacobs, David
    Trevisan, Vilmar
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2024, 40 : 81 - 139
  • [47] The eigenvalues of very sparse random symmetric matrices
    Juozulynas A.
    [J]. Lithuanian Mathematical Journal, 2004, 44 (1) : 62 - 70
  • [48] On the Geometry of the Set of Symmetric Matrices with Repeated Eigenvalues
    Breiding P.
    Kozhasov K.
    Lerario A.
    [J]. Arnold Mathematical Journal, 2018, 4 (3-4) : 423 - 443
  • [49] Homotopy method for the eigenvalues of symmetric tridiagonal matrices
    Brockman, Philip
    Carson, Timothy
    Cheng, Yun
    Elgindi, T. M.
    Jensen, K.
    Zhoun, X.
    Elgindi, M. B. M.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 237 (01) : 644 - 653
  • [50] Factorizations and eigenvalues of fibonacci and symmetric fibonacci matrices
    Lee, GY
    Kim, JS
    Lee, SG
    [J]. FIBONACCI QUARTERLY, 2002, 40 (03): : 203 - 211
12345