An Accelerated Jacobi-Gradient Iterative Algorithm to Solve the Matrix Equation \({\varvec{A}}\boldsymbol{ Z}-\overline{\boldsymbol{ Z}}{\varvec{B}}={\varvec{C}}\)

Abstract

In this paper, we present an accelerated Jacobi-gradient-based iterative AJGI algorithm to solve the matrix equation \(A{ Z}-\overline{ Z}B=C\), which is based on algorithms presented by Bayoumi (Appl Math Inf Sci, 2021). The iterative solution converges to the exact solution for any initial value under appropriate assumptions. Numerical examples are provided to support the suggested approach and verify its effectiveness and accuracy when compared to a recent one previously described in Bayoumi (Appl Math Inf Sci, 2021).