Gradient-based iteration for a class of matrix equations
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 algorithms are effective for any initial values.The analysis indicates that if the matrix equation has a unique solution,then the iterative solutions converge to the exact one for any initial value under proper conditions.A numerical example is provided to illustrate the effectiveness of the proposed algorithm.
Gradient iteration Hierarchical identification principle Matrix equation Convergence factor
Huamin Zhang
Mathematics and Physics Department,Bengbu College,Bengbu 233000,PR China
国际会议
长沙
英文
1201-1205
2014-05-31（万方平台首次上网日期，不代表论文的发表时间）