Acceleration of contour integration techniques by rational Krylov subspace methods

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• 作者：T. Gö ; ckler ^{tanja.goeckler@kit.edu} ; V. Grimm ; ^{volker.grimm@kit.edu}
• 关键词：65F60 ; 65L04 ; 65L70 ; 65M22
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：316
• 期：Complete
• 页码：133-142
• 全文大小：689 K
• 卷排序：316

文摘

We suggest a rational Krylov subspace approximation for products of matrix functions and a vector appearing in exponential integrators. We consider matrices with a field-of-values in a sector lying in the left complex half-plane. The choice of the poles for our method is suggested by a fixed rational approximation based on contour integration along a hyperbola around the sector. Compared to the fixed approximation, our rational Krylov subspace method exhibits an accelerated and more stable convergence of order O(e−Cn)O(e−Cn).