A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functions
A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functions
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DOI：
10.1007/s10543-013-0420-x
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发表时间：
2013-01
影响因子：
1.5
通讯作者：
S. Güttel;L. Knizhnerman
中科院分区：
文献类型：
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作者：
S. Güttel;L. Knizhnerman
有理Arnoldi是一个强大的方法来逼近大型稀疏矩阵乘以向量的函数。渐近最优参数的选择是该方法快速收敛的关键。我们提出并研究了一种新的策略，用于自动参数选择时，要近似的函数是Cauchy-Stieltjes（或马尔可夫）型，如矩阵平方根或对数。这种方法的性能证明了涉及对称和非对称矩阵的数值例子。这些例子表明，我们的黑盒方法执行至少一样好，通常更好，作为标准的理性Arnoldi方法与参数手动优化一个给定的矩阵。
Rational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present and investigate a novel strategy for the automated parameter selection when the function to be approximated is of Cauchy–Stieltjes (or Markov) type, such as the matrix square root or the logarithm. The performance of this approach is demonstrated by numerical examples involving symmetric and nonsymmetric matrices. These examples suggest that our black-box method performs at least as well, and typically better, as the standard rational Arnoldi method with parameters being manually optimized for a given matrix.