Generalized Rational Krylov Decompositions with an Application to Rational Approximation
Generalized Rational Krylov Decompositions with an Application to Rational Approximation
复制标题
广义有理 Krylov 分解及其在有理逼近中的应用
DOI：
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发表时间：
2015
影响因子：
1.5
通讯作者：
S. Güttel
中科院分区：
文献类型：
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作者：
Mario Berljafa;S. Güttel
广义有理克雷洛夫分解是在某些条件下与有理克雷洛夫空间相关的矩阵关系。我们研究了此类分解的代数性质，并提出了有理 Krylov 空间的隐式 Q 定理。有理 Krylov 分解的变换允许更改有理 Krylov 空间的极点而无需重新计算，并且针对此任务提出了两种算法。使用这种变换，我们开发了一种用于有理最小二乘拟合的有理 Krylov 方法。数值实验表明该方法收敛速度快且鲁棒。提供了一个 MATLAB 工具箱，其中包含所提出的算法和实验的实现。
Generalized rational Krylov decompositions are matrix relations which, under certain conditions, are associated with rational Krylov spaces. We study the algebraic properties of such decompositions and present an implicit Q theorem for rational Krylov spaces. Transformations on rational Krylov decompositions allow for changing the poles of a rational Krylov space without recomputation, and two algorithms are presented for this task. Using such transformations we develop a rational Krylov method for rational least squares fitting. Numerical experiments indicate that the proposed method converges fast and robustly. A MATLAB toolbox with implementations of the presented algorithms and experiments is provided.