Iterative algorithms for X+A^TX^∿A=I by using the hierarchical identification principle

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• 作者：Huamin Zhang ^{zhangeasymail@126.com" class="auth_mail" title="E-mail the corresponding author} ; Feng Ding ; ^{fding@jiangnan.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of The Franklin Institute
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：353
• 期：5
• 页码：1132-1146
• 全文大小：365 K

文摘

By using the hierarchical identification principle and introducing the convergence factor and the iterative matrix, a family of inversion-free iterative algorithms is proposed for solving nonlinear matrix equations X+A^TX⁻¹A=I$\mathit{X}+{\mathit{A}}^{\mathrm{T}}{\mathit{X}}^{-1}\mathit{A}=\mathit{I}$. The convergence is proved and the convergence speed is analyzed. The suggested iterative algorithm includes some previous algorithms as its special cases. Two numerical examples are given to illustrate the proposed algorithms. Theoretical analysis and numerical examples show that for appropriate convergence factors, the proposed algorithms are more efficient than the existing inversion-free iterative algorithms.