Computing enclosures for the matrix Mittag-Leffler function
Computing enclosures for the matrix Mittag-Leffler function
复制标题
矩阵 Mittag-Leffler 函数的计算外壳
DOI：
10.1007/s10915-021-01447-6
复制
发表时间：
2021
影响因子：
2.5
通讯作者：
Shinya Miyajima
中科院分区：
文献类型：
--
作者：
Longrio Platil;Tamaki Tanaka;Shinya Miyajima
提出了两种数值计算包含双参数Mittag-Leffler（ML）函数的区间矩阵的算法。我们首先提出了一种计算纯量ML函数外壳的算法。然后，利用标量算法和验证块对角化来开发所提出的两种算法。第一种算法依赖于数值谱分解。如果第二个参数不太小，该算法的代价只是标量算法的三次方加。第二个算法是基于数值Jordan分解，也可以应用于亏损矩阵。该算法的代价是四次函数加标量算法的代价。数值实验说明了一个分数阶微分方程的应用。
We propose two algorithms for numerically calculating interval matrices including two-parameter matrix Mittag–Leffler (ML) functions. We first present an algorithm for computing enclosures for scalar ML functions. Then, the two proposed algorithms are developed by exploiting the scalar algorithm and verified block diagonalization. The first algorithm relies on a numerical spectral decomposition. The cost of this algorithm is only cubic plus that of the scalar algorithm if the second parameter is not too small. The second algorithm is based on a numerical Jordan decomposition, and can also be applied to defective matrices. The cost of this algorithm is quartic plus that of the scalar algorithm. A numerical experiment illustrates an application to a fractional differential equation.