A fast eigenvalue algorithm for Hankel matrices

被引：17
|
作者：
Luk, FT [1 ]
Qiao, SZ
机构：
[1] Rensselaer Polytech Inst, Dept Comp Sci, Troy, NY 12180 USA
[2] McMaster Univ, Dept Comp & Software, Hamilton, ON L8S 4K1, Canada
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 316卷 / 1-3期
关键词：
Hankel matrix; toeplitz matrix; circulant matrix; fast Fourier transform; Lanczos tridiagonalization; eigenvalue decomposition; complex-symmetric matrix; complex-orthogonal transformations;
D O I：
10.1016/S0024-3795(00)00084-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present an algorithm that can find all the eigenvalues of an n x n complex Hankel matrix in O(n(2) log n) operations. Our scheme consists of an O(n(2) log n) Lanczos-type tridiagonalization procedure and an O(n) QR-type diagonalization method. (C) 2000 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：171 / 182
页数：12
相关论文
共 50 条
  • [1] A fast eigenvalue algorithm for Hankel matrices
    Luk, FT
    Qiao, S
    ADVANCED SIGNAL PROCESSING ALGORITHMS, ARCHITECTURES, AND IMPLEMENTATIONS VIII, 1998, 3461 : 249 - 256
  • [2] Analysis of a fast Hankel eigenvalue algorithm
    Luk, FT
    Qiao, SZ
    ADVANCED SIGNAL PROCESSING ALGORITHMS, ARCHITECTURES,AND IMPLEMENTATIONS IX, 1999, 3807 : 324 - 333
  • [3] A fast eigenvalue algorithm for Pascal matrices
    Wang Xiang
    Zhou Jituan
    APPLIED MATHEMATICS AND COMPUTATION, 2006, 183 (02) : 711 - 716
  • [4] A fast singular value algorithm for Hankel matrices
    Luk, FT
    Qiao, SZ
    ADVANCED SIGNAL PROCESSING ALGORITHMS, ARCHITECTURES, AND IMPLEMENTATIONS XI, 2001, 4474 : 254 - 261
  • [5] The Smallest Eigenvalue of Hankel Matrices
    Berg, Christian
    Szwarc, Ryszard
    CONSTRUCTIVE APPROXIMATION, 2011, 34 (01) : 107 - 133
  • [6] The Smallest Eigenvalue of Hankel Matrices
    Christian Berg
    Ryszard Szwarc
    Constructive Approximation, 2011, 34 : 107 - 133
  • [7] Eigenvalue estimates for Hankel matrices
    Zamarashkin, NL
    Tyrtyshnikov, EE
    SBORNIK MATHEMATICS, 2001, 192 (3-4) : 537 - 550
  • [8] A fast symmetric SVD algorithm for square Hankel matrices
    Xu, Wei
    Qiao, Sanzheng
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (2-3) : 550 - 563
  • [9] The smallest eigenvalue of large Hankel matrices
    Zhu, Mengkun
    Chen, Yang
    Emmart, Niall
    Weems, Charles
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 334 : 375 - 387
  • [10] A FAST PARALLEL ALGORITHM FOR EIGENVALUE PROBLEM OF JACOBI MATRICES
    FRUMKIN, MA
    LECTURE NOTES IN COMPUTER SCIENCE, 1988, 324 : 291 - 299
12345