Developing Bi-CG and Bi-CR methods to solve generalized Sylvester-transpose matrix equations

被引：22

作者：

Hajarian M. ^{[1
]}

机构：

[1] Department of Mathematics, Shahid Beheshti University, Evin, Tehran, 19839, General Campus

来源：

International Journal of Automation and Computing | 2014年 / 11卷 / 01期

关键词：

bi-conjugate gradients (Bi-CG) method; bi-conjugate residual (Bi-CR) method; Sylvester matrix equation; iterative method; Linear systems;

D O I：

10.1007/s11633-014-0762-0

中图分类号：

学科分类号：

摘要：

The bi-conjugate gradients (Bi-CG) and bi-conjugate residual (Bi-CR) methods are powerful tools for solving nonsymmetric linear systems Ax = b. By using Kronecker product and vectorization operator, this paper develops the Bi-CG and Bi-CR methods for the solution of the generalized Sylvester-transpose matrix equation Σ i=1 p (A i XB i + C i X T D i) = E (including Lyapunov, Sylvester and Sylvester-transpose matrix equations as special cases). Numerical results validate that the proposed algorithms are much more efficient than some existing algorithms. © 2014 Institute of Automation, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.

引用

页码：25 / 29

页数：4

共 32 条

[1]

Duan G.R., Parametric approaches for eigenstructure assignment in high-order linear systems, International Journal of Control, Automation, and Systems, 3, 3, pp. 419-429, (2005)

[2]

Zhou B., Lam J., Duan G.R., On Smith-type iterative algorithms for the Stein matrix equation, Applied Mathematics Letters, 22, 7, pp. 1038-1044, (2009)

[3]

Duan G.R., Patton R.J., Robust fault detection using Luenberger-type unknown input observers - A parametric approach, International Journal of Systems Science, 32, 4, pp. 533-540, (2001)

[4]

Fletcher L.R., Kuatsky J., Nichols N.K., Eigenstructure assignment in descriptor systems, IEEE Transactions on Automatic Control, 31, pp. 1138-1141, (1986)

[5]

LaSalle L.P., Lefschetz S., Stability by Liapunov's Direct Method: With Applications, (1961)

[6]

Bernstein D.S., Hyland D.C., The optimal projection equations for reduced-order state estimation, IEEE Transactions on Automatic Control, 30, 6, pp. 583-585, (1985)

[7]

Laub A.J., A Schur method for solving algebraic Riccati equations, IEEE Transactions on Automatic Control, 24, 6, pp. 913-921, (1979)

[8]

Ding J., Liu Y.J., Ding F., Iterative solutions to matrix equations of the form AiXBi = Fi, Computers and Mathematics with Applications, 59, 11, pp. 3500-3507, (2010)

[9]

Kyrchei I., Analogs of Cramer' rule for the minimum norm least squares solutions of some matrix equations, Applied Mathematics and Computation, 218, 11, pp. 6375-6384, (2012)

[10]

Niu Q., Wang X., Lu L.Z., A relaxed gradient based algorithm for solving sylvester equations, Asian Journal of Control, 13, 3, pp. 461-464, (2011)

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