Abstract
Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.
Highlights
How to solve a matrix equation is a focus question of the applied mathematics and engineering fields [1] [2]
For a complex matrix A ∈ m×n, it can be exclusive signified as A= A1 + iA2, where A1, A2 ∈ m×n are two real matrices
According to the hierarchical identification principle, we introduce the intermediate matrices: F11 := Ψ1 + A11 X1B11, F12 := Ψ1 + C11 X1D11, F13 := Ψ1 + G11 X1T H11, F14 := Ψ1 + M11 X1H N11, (16) (17)
Summary
How to solve a matrix equation is a focus question of the applied mathematics and engineering fields [1] [2]. Based on the classical iterative algorithm and the hierarchical identification principle, some gradient-based and least squares based iterative algorithms were established. This method has been developed in solving other coupled matrix equations [3]. The gradient-based iterative algorithm for solving a class of complex matrix equations was established and the sufficient condi-. Inspired by the above work, this paper discusses gradient-based iterative algorithm for a coupled complex conjugate and transpose matrix equation.
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