An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations

作者：Yin, Feng^*; Huang, Guang-Xin

来源：Journal of Applied Mathematics, 2012, 152805.

DOI：10.1155/2012/152805

• LEAST-SQUARES SOLUTIONS
• RECURSIVE BLOCKED ALGORITHMS
• SOLVING TRIANGULAR SYSTEMS
• SKEW SYMMETRIC-SOLUTIONS
• OPTIMAL APPROXIMATION
• PART II
• AXB
• CYD

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations (XB - CYD, EXF - GYH) = (M, N), which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y. When the matrix equations are consistent, for any initial generalized reflexive matrix pair [X-1, Y-1], the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation generalized reflexive solution pair [(X) over cap, (Y) over cap] to a given matrix pair [X-0, Y-0] in Frobenius norm corresponding can be derived by finding the least-norm generalized reflexive solution [(X) over tilde*, (Y) over tilde*] of a new corresponding generalized coupled Su;vester matrix equation pair (A (X) over tildeB - C (Y) over tildeD, E (X) over tildeF - G (Y) over tildeH) = ((M) over tilde(N) over tilde), where (M) over tilde = M - AX(0)B _ CY0D, (N) over tilde = N - EX0F + GY(0)H. Several numerical examples are given to show the effectiveness of the presented iterative algorithm.

• 出版日期2012
• 单位成都理工大学; 四川轻化工大学