Numerically stable improved Chebyshev-Halley type schemes for matrix sign function

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• 作者：Alicia Cordero^a ; ^{acordero@mat.upv.es} ; F. Soleymani^b ; ^{fazlollah.soleymani@gmail.com} ; Juan R. Torregrosa^a ; ^{jrtorre@mat.upv.es} ; M. Zaka Ullah^c ; ^{mzhussain@kau.edu.sa}
• 关键词：Matrix sign function ; Stability ; Iterative methods ; Chebyshev&ndash ; Halley family ; Eigenvalues
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：189-198
• 全文大小：1177 K
• 卷排序：318

文摘

A general family of iterative methods including a free parameter is derived and proved to be convergent for computing matrix sign function under some restrictions on the parameter. Several special cases including global convergence behavior are dealt with. It is analytically shown that they are asymptotically stable. A variety of numerical experiments for matrices with different sizes is considered to show the effectiveness of the proposed members of the family.