A Hessenberg method for the numerical solutions to types of block Sylvester matrix equation

被引：6
作者：
Ramadan, Mohamed A. [1 ]
El-Shazly, Naglaa M. [1 ]
Selim, Basem I. [1 ]
机构：
[1] Menoufia Univ, Fac Sci, Dept Math, Shibin Al Kawm, Egypt
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2010年 / 52卷 / 9-10期
关键词：
Sylvester equation; Block linear systems; Direct methods; Similarity transformation; KRYLOV-SUBSPACE METHODS;
D O I：
10.1016/j.mcm.2010.06.042
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, we propose a new algorithm to solve the Sylvester matrix equation XA + BX = C. The technique consists of orthogonal reduction of the matrix A to a block upper Hessenberg form P(T)AP = H and then solving the reduced equation, YH + BY = C for Y through recurrence relation, where Y = XP, and C' = CP. We then recover the solution of the original problem via the relation X = YP(T). The numerical results show the accuracy and the efficiency of the proposed algorithm. In addition, how the technique described can be applied to other matrix equations was shown. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1716 / 1727
页数：12
相关论文
共 12 条
  • [1] ALGORITHM - SOLUTION OF MATRIX EQUATION AX+XB = C
    BARTELS, RH
    STEWART, GW
    [J]. COMMUNICATIONS OF THE ACM, 1972, 15 (09) : 820 - &
  • [2] Datta B. N., 1986, Computational and Combinatorial Methods in Systems Theory, P201
  • [3] Datta B.N., 2003, Numerical Methods for Linear Control Systems and Analysis
  • [4] Krylov subspace methods for large-scale matrix problems in control
    Datta, BN
    [J]. FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE, 2003, 19 (07): : 1253 - 1263
  • [5] Block Krylov subspace methods for solving large Sylvester equations
    El Guennouni, A
    Jbilou, K
    Riquet, AJ
    [J]. NUMERICAL ALGORITHMS, 2002, 29 (1-3) : 75 - 96
  • [6] Golub G. H., 1996, MATRIX COMPUTATIONS
  • [7] HESSENBERG-SCHUR METHOD FOR THE PROBLEM AX+XB=C
    GOLUB, GH
    NASH, S
    VANLOAN, C
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1979, 24 (06) : 909 - 913
  • [8] KRYLOV-SUBSPACE METHODS FOR THE SYLVESTER EQUATION
    HU, DY
    REICHEL, L
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 172 : 283 - 313
  • [9] Kaabi A, 2007, APPL MATH SCI, V1, P2895
  • [10] Monsalve M, 2008, COMPUT APPL MATH, V27, P47, DOI 10.1590/S1807-03022008000100003
12