Computing the logarithm of a symmetric positive definite matrix

被引：12
|
作者：
Lu, YY [1 ]
机构：
[1] City Univ Hong Kong, Dept Math, Kowloon, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 1998年 / 26卷 / 04期
关键词：
matrix logarithm; Pade approximation; tridiagonal reduction;
D O I：
10.1016/S0168-9274(97)00103-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A numerical method for computing the logarithm of a symmetric positive definite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pade approximations to the logarithm of the tridiagonal matrix. Theoretical studies and numerical experiments indicate that the method is quite efficient when the matrix is not very ill-conditioned. (C) 1998 IMACS/Elsevier Science B.V.
引用
收藏
页码：483 / 496
页数：14
相关论文
共 50 条
  • [41] A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix
    Boutsidis, Christos
    Drineas, Petros
    Kambadur, Prabhanjan
    Kontopoulou, Eugenia-Maria
    Zouzias, Anastasios
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 533 : 95 - 117
  • [42] Locally Preserving Projection on Symmetric Positive Definite Matrix Lie Group
    Li, Yangyang
    2017 24TH IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP), 2017, : 1217 - 1221
  • [43] SYMMETRIC POSITIVE DEFINITE MATRICES
    JAGERS, AA
    AMERICAN MATHEMATICAL MONTHLY, 1988, 95 (03): : 261 - 262
  • [44] On A High Order Algorithm Converging To The mth Root Of A Positive Matrix And Application For Computing The Matrix Logarithm
    Al-harbi, Nawal Helal
    Raissouli, Mustapha
    Mashat, Daoud Suleiman
    APPLIED MATHEMATICS E-NOTES, 2023, 23 : 229 - 236
  • [45] A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations
    Zhang, Huamin
    Ding, Feng
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2014, 351 (01): : 340 - 357
  • [46] GRAPH PARTITIONING USING MATRIX VALUES FOR PRECONDITIONING SYMMETRIC POSITIVE DEFINITE SYSTEMS
    Vecharynski, Eugene
    Saad, Yousef
    Sosonkina, Masha
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2014, 36 (01): : A63 - A87
  • [47] Preconditioned Lanczos methods for the minimum eigenvalue of a symmetric positive definite Toeplitz matrix
    Ng, MK
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (06): : 1973 - 1986
  • [48] Nonparametric matrix regression function estimation over symmetric positive definite matrices
    Kwan-Young Bak
    Kwang-Rae Kim
    Peter T. Kim
    Ja-Yong Koo
    Changyi Park
    Hongtu Zhu
    Journal of the Korean Statistical Society, 2021, 50 : 795 - 817
  • [49] ON DISTRIBUTION OF LATENT ROOTS OF A POSITIVE DEFINITE RANDOM SYMMETRIC MATRIX .I.
    HAYAKAWA, T
    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1969, 21 (01) : 1 - &
  • [50] Numerical algorithm for estimating a conditioned symmetric positive definite matrix under constraints
    Livne, Oren E.
    Castellano, Katherine E.
    Mccaffrey, Dan F.
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2024, 31 (05)
12345