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In this paper, we prove the convergence and determine the best convergence factor of the gradient-based iterative algorithm for the equation Ax = b by analyzing the eigenvalues of the relevant matrices. A new property of eigenvalues related to the symmetric positive definite matrix is established. By using this property, we obtain a family of iterative algorithms for the linear matrix equation and...
In this paper, by constructing an objective function and using the gradient search, three gradient-based iterations are established for solving generalized coupled Sylvester matrix equations, when the related matrices are full-column rank, full-row rank or rank deficiency. It is proved that these three gradient-based iterative algorithms are convergent for any initial iterative values. By analyzing...
In this paper, an iterative algorithm is established for solving a class of matrix equations with complex unknowns. By using the hierarchical identification principle, the gradient-based iterative algorithms are constructed to solve the equation AXB + CXHD = F and the coupled equations A1XB1 + A2XHB2 = F1 and C1XD1 + C2XHD2 = F2. The the convergence factor is presented to guarantee that the iterative...
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