user

Estimation of the eigenvalues and the smallest singular value of matrices

被引：22
|
作者：
Zou, Limin [1 ]
Jiang, Youyi [1 ]
机构：
[1] Chongqing Three Gorges Univ, Coll Math & Comp Sci, Chongqing 404000, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 433卷 / 06期
关键词：
Eigenvalues; Disk; Norm; Singular values; BOUNDS;
D O I：
10.1016/j.laa.2010.05.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to discuss the estimation of eigenvalues and the smallest singular value of matrices. Firstly, we prove that all the eigenvalues of arbitrarily complex matrix are located in one closed disk around trM/n of radius root n - 1/n (parallel to M parallel to(2)(F) - vertical bar trM vertical bar(2)/n - max(1 <= k <= n-1) (parallel to B(kx(n-k))parallel to(F) - parallel to C((n-k)xk)parallel to(F))(2)). Secondly, we present a lower bound for the smallest singular value of matrices. Finally, we give some numerical examples which will show the effectiveness of our results. Crown copyright (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：1203 / 1211
页数：9
相关论文
共 50 条
  • [1] Estimation of lower bound for the smallest singular value enclosure of interval matrices
    Singh, Sarishti
    Panda, Geetanjali
    [J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2024,
  • [2] On the smallest singular value of symmetric random matrices
    Jain, Vishesh
    Sah, Ashwin
    Sawhney, Mehtaab
    [J]. COMBINATORICS PROBABILITY & COMPUTING, 2022, 31 (04): : 662 - 683
  • [3] Smallest singular value of sparse random matrices
    Litvak, Alexander E.
    Rivasplata, Omar
    [J]. STUDIA MATHEMATICA, 2012, 212 (03) : 195 - 218
  • [4] Smallest singular value of random matrices with independent columns
    Adamczak, Radoslaw
    Guedon, Olivier
    Litvak, Alexander
    Pajor, Alain
    Tomczak-Jaegermann, Nicole
    [J]. COMPTES RENDUS MATHEMATIQUE, 2008, 346 (15-16) : 853 - 856
  • [5] TWO LOWER BOUNDS FOR THE SMALLEST SINGULAR VALUE OF MATRICES
    Liu, Wushuang
    Hu, Xingkai
    Wang, Yaoqun
    Yi, Yuan
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2023, 17 (03): : 885 - 891
  • [6] A remark on the smallest singular value of powers of Gaussian matrices
    Huang, Han
    Tikhomirov, Konstantin
    [J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2020, 25
  • [7] On the decay of the smallest singular value of submatrices of rectangular matrices
    Liu, Yang
    Wang, Yang
    [J]. ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2016, 9 (04)
  • [8] On some lower bounds for smallest singular value of matrices
    Lin, Minghua
    Xie, Mengyan
    [J]. APPLIED MATHEMATICS LETTERS, 2021, 121
  • [9] THE SMALLEST SINGULAR VALUE OF INHOMOGENEOUS SQUARE RANDOM MATRICES
    Livshyts, Galyna, V
    Tikhomirov, Konstantin
    Vershynin, Roman
    [J]. ANNALS OF PROBABILITY, 2021, 49 (03): : 1286 - 1309
  • [10] Estimation of ∥A-1∥∞ and the smallest singular value
    Huang, Ting-Zhu
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 55 (06) : 1075 - 1080
12345