Interlacing properties of tridiagonal symmetric matrices with applications to parallel computing

被引：7
作者：
BarOn, I [1 ]
机构：
[1] TECHNION ISRAEL INST TECHNOL, DEPT COMP SCI, IL-32000 HAIFA, ISRAEL
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1996年 / 17卷 / 03期
关键词：
symmetric; tridiagonal; eigenvalues; parallel algorithms;
D O I：
10.1137/S0895479893252003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we present new interlacing properties for the eigenvalues of an unreduced tridiagonal symmetric matrix in terms of its leading and trailing submatrices. The results stated in Hill and Parlett [SIAM J. Matrix Anal, Appl., 13 (1992), pp. 239-247] are hereby improved. We further extend our results to reduced symmetric tridiagonal matrices and to specially structured full symmetric matrices. We then present new fast and efficient parallel algorithms for computing a few eigenvalues of symmetric tridiagonal matrices of very large order.
引用
收藏
页码：548 / 562
页数：15
相关论文
共 15 条
  • [1] A FAST AND STABLE PARALLEL QR ALGORITHM FOR SYMMETRICAL TRIDIAGONAL MATRICES
    BARON, I
    CODENOTTI, B
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 220 : 63 - 95
  • [2] BARON I, 1994, 832 COMP SCI DEP
  • [3] BARON I, 1992, 726 COMP SCI DEP
  • [4] Cullum J. K., 1985, LANCZOS ALGORITHMS L
  • [5] CUPPEN JJM, 1981, NUMER MATH, V36, P177, DOI 10.1007/BF01396757
  • [6] A FULLY PARALLEL ALGORITHM FOR THE SYMMETRICAL EIGENVALUE PROBLEM
    DONGARRA, JJ
    SORENSEN, DC
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1987, 8 (02): : S139 - S154
  • [7] Golub G, 2013, Matrix Computations, V4th
  • [8] HILL RO, 1992, SIAM J MATRIX ANAL A, V13, P239
  • [9] Horn R A., 2012, Matrix Analysis, V2nd edn, DOI 10.1017/CBO9780511810817
  • [10] Kahan W., 1966, Accurate eigenvalues of a symmetric tri-diagonal matrix
12