Decay bounds for the numerical quasiseparable preservation in matrix functions

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• 作者：Stefano Massei^a ; ^{stefano.massei@sns.it} ; Leonardo Robol^b ; ^{leonardo.robol@cs.kuleuven.be}
• 关键词：15A16 ; 65F60 ; 65D32 ; 30C30 ; 65E05
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：516
• 期：Complete
• 页码：212-242
• 全文大小：712 K
• 卷排序：516

文摘

Given matrices A and B   such that B=f(A)B=f(A), where f(z)f(z) is a holomorphic function, we analyze the relation between the singular values of the off-diagonal submatrices of A and B. We provide a family of bounds which depend on the interplay between the spectrum of the argument A   and the singularities of the function. In particular, these bounds guarantee the numerical preservation of quasiseparable structures under mild hypotheses. We extend the Dunford–Cauchy integral formula to the case in which some poles are contained inside the contour of integration. We use this tool together with the technology of hierarchical matrices (HH-matrices) for the effective computation of matrix functions with quasiseparable arguments.