Computation of matrix gamma function
Computation of matrix gamma function
复制标题
矩阵伽玛函数的计算
DOI：
10.1007/s10543-018-00744-1
复制
发表时间：
2018
影响因子：
1.5
通讯作者：
A. Sadeghi
中科院分区：
文献类型：
--
作者：
J. R. Cardoso;A. Sadeghi
矩阵函数在科学和工程中有着重要的作用。其中一个基本的矩阵函数，这是特别重要的，因为它与某些矩阵微分方程和其他特殊的矩阵函数，是矩阵伽玛函数。本文主要研究该函数的数值计算。众所周知的技术的标量伽玛函数，如Lanczos，Spouge和斯特林近似，扩展到矩阵的情况下。这种扩展提出了许多具有挑战性的问题，并在矩阵函数的计算中使用的几种策略，如舒尔分解和块Parlett递归，需要纳入，使方法更有效。我们还提出了第四种技术的基础上的倒数伽马函数，被证明是有竞争力的其他三种方法在精度方面，具有丰富的矩阵乘法的优势。所提出的方法的优点和缺点说明了一组数值例子。截断误差的界和与矩阵伽玛函数相关的其他界也将被讨论。
Matrix functions have a major role in science and engineering. One of the fundamental matrix functions, which is particularly important due to its connections with certain matrix differential equations and other special matrix functions, is the matrix gamma function. This research article focus on the numerical computation of this function. Well-known techniques for the scalar gamma function, such as Lanczos, Spouge and Stirling approximations, are extended to the matrix case. This extension raises many challenging issues and several strategies used in the computation of matrix functions, like Schur decomposition and block Parlett recurrences, need to be incorporated to make the methods more effective. We also propose a fourth technique based on the reciprocal gamma function that is shown to be competitive with the other three methods in terms of accuracy, with the advantage of being rich in matrix multiplications. Strengths and weaknesses of the proposed methods are illustrated with a set of numerical examples. Bounds for truncation errors and other bounds related with the matrix gamma function will be discussed as well.
影响因子：
3.1
作者：
Al-Mohy, Awad H.;Higham, Nicholas J.
通讯作者：
Higham, Nicholas J.