Fast Taylor polynomial evaluation for the computation of the matrix cosine
Fast Taylor polynomial evaluation for the computation of the matrix cosine
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用于计算矩阵余弦的快速泰勒多项式评估
DOI：
10.1016/j.cam.2018.12.041
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
E. Defez
中科院分区：
文献类型：
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作者：
J. Sastre;J. Ibáñez;P. Alonso;Jesús Peinado;E. Defez
本文介绍了一种计算矩阵余弦的新方法。该方法基于泰勒近似的矩阵多项式评价方法和混合前向和后向误差分析。矩阵多项式评估方法允许评估矩阵余弦函数的泰勒多项式近似比使用帕特森-斯托克迈耶方法更有效。提供了新算法的顺序Matlab实现，比现有算法具有更好的效率和准确性。此外，我们还在Matlab中提供了一个可以轻松高效地使用NVIDIA gpu的实现。
In this work we introduce a new method to compute the matrix cosine. It is based on recent new matrix polynomial evaluation methods for the Taylor approximation and a mixed forward and backward error analysis. The matrix polynomial evaluation methods allow to evaluate the Taylor polynomial approximation of the matrix cosine function more efficiently than using Paterson–Stockmeyer method. A sequential Matlab implementation of the new algorithm is provided, giving better efficiency and accuracy than state-of-the-art algorithms. Moreover, we provide an implementation in Matlab that can use NVIDIA GPUs easily and efficiently.
DOI：
10.1137/140973979
发表时间：
2015-02
期刊：
SIAM J. Sci. Comput.
影响因子：
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作者：
Awad H. Al-Mohy;N. Higham;S. Relton
通讯作者：
Awad H. Al-Mohy;N. Higham;S. Relton