An iterative algorithm for the least Frobenius norm Hermitian and generalized skew Hamiltonian solutions of the generalized coupled Sylvester-conjugate matrix equations

被引：6

作者：

Huang, Baohua ^{[1
]}

Ma, Changfeng ^{[1
]}

机构：

[1] Fujian Normal Univ, Coll Math & Informat, Fujian Key Lab Math Anal & Applicat, Fuzhou 350117, Fujian, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2018年 / 78卷 / 04期

关键词：

Iterative method; Generalized coupled Sylvester-conjugate matrix equations; Hermitian and generalized skew hamiltonian solution; Least Frobenius norm solution; Numerical experiments; AXB PLUS CYD; SQUARES SOLUTIONS; RICCATI EQUATION; APPROXIMATION; REFLEXIVE;

D O I：

10.1007/s11075-017-0423-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The iterative method of the generalized coupled Sylvester-conjugate matrix equations over Hermitian and generalized skew Hamiltonian solution is presented. When these systems of matrix equations are consistent, for arbitrary initial Hermitian and generalized skew Hamiltonian matrices X (j) (1), j = 1,2,ai , l, the exact solutions can be obtained by iterative algorithm within finite iterative steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm Hermitian and generalized skew Hamiltonian solution of the problem. Finally, numerical examples are presented to demonstrate the proposed algorithm is efficient.

引用

页码：1271 / 1301

页数：31

共 45 条

[1]

[Anonymous], 1996, ALGORITHMS LINEAR QU

[2] The solvability conditions for the inverse eigenvalue problem of Hermitian and generalized skew-Hamiltonian matrices and its approximation [J].

Bai, ZJ .

INVERSE PROBLEMS, 2003, 19 (05) :1185-1194

[3] The coupled Sylvester-transpose matrix equations over generalized centro-symmetric matrices [J].

Beik, Fatemeh Panjeh Ali ;

Salkuyeh, Davod Khojasteh .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2013, 90 (07) :1546-1566

[4] On the global Krylov subspace methods for solving general coupled matrix equations [J].

Beik, Fatemeh Panjeh Ali ;

Salkuyeh, Davod Khojasteh .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (12) :4605-4613

[5]

Bittanti S., 2012, The Riccati Equation

[6] PARALLEL COMPUTATION OF THE SOLUTIONS OF COUPLED ALGEBRAIC LYAPUNOV EQUATIONS [J].

BORNO, I .

AUTOMATICA, 1995, 31 (09) :1345-1347

[7] An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation [J].

Dehghan, Mehdi ;

Hajarian, Masoud .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (02) :571-588

[8] Construction of an iterative method for solving generalized coupled Sylvester matrix equations [J].

Dehghan, Mehdi ;

Hajarian, Masoud .

TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2013, 35 (08) :961-970

[9] On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations [J].

Dehghan, Mehdi ;

Hajarian, Masoud .

LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (11) :1281-1309

[10] The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices [J].

Dehghan, Mehdi ;

Hajarian, Masoud .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2012, 43 (08) :1580-1590

← 1 2 3 4 5 →