Generalized Schultz iterative methods for the computation of outer inverses

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• 作者：Marko D. Petkovi膰 ^{dexterofnis@gmail.com" class="auth_mail}
• 关键词：Moore&ndash ; Penrose inverse ; Drazin inverse ; Outer inverse ; Iterative methods ; Convergence ; Schultz method
• 刊名：Computers and Mathematics with Applications
• 出版年：June 2014
• 年：2014
• 卷：67
• 期：10
• 页码：1837-1847
• 全文大小：427 K

文摘

We consider a general matrix iterative method of the type X_k+1=X_kp(AX_k)$X_{k+1}=X_{k}p\left(A{X}_k\right)$ for computing an outer inverse f2ceea9237347ad">$A_{\mathcal{R}\left(G\right),\mathcal{N}\left(G\right)}^{\left(2\right)}$, for given matrices A∈C^m×n$A\in {\mathbb{C}}^{m\times n}$ and G∈C^n×m$G\in {\mathbb{C}}^{n\times m}$ such that AR(G)⊕N(G)=C^m$A\mathcal{R}\left(G\right)\oplus \mathcal{N}\left(G\right)={\mathbb{C}}^m$. Here fff2bf190c630f307eba20d8" title="Click to view the MathML source">p(x)$p\left(x\right)$ is an arbitrary polynomial of degree d$d$. The convergence of the method is proven under certain necessary conditions and the characterization of all methods having order 2cdc880214377f9cde2d0ac9aaf70b0" title="Click to view the MathML source">r$r$ is given. The obtained results provide a direct generalization of all known iterative methods of the same type. Moreover, we introduce one new method and show a procedure how to improve the convergence order of existing methods. This procedure is demonstrated on one concrete method and the improvement is confirmed by numerical examples.