指数积分器中矩阵函数的并行计算及其对向量的作用

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-24 DOI:10.1016/j.cam.2025.117090

Sergio Blanes

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引用次数: 0

摘要

我们提出了一类新的方法来计算矩阵的函数或它们对向量的作用，这些方法适用于并行编程，并能提高指数积分器的性能。求解适当的并行线性方程组（或计算几个矩阵的逆），并将结果进行适当的线性组合，使我们能够获得对矩阵所需函数的新的高阶近似。给出了一种误差分析方法来获得前向和后向误差边界。每个方法的系数取决于处理器的数量，可以调整，以提高精度，稳定性或减少方法的舍入误差。我们通过显式构造一些方法来说明这一过程，然后在几个数值例子上进行了测试。

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Parallel Computation of functions of matrices and their action on vectors for exponential integrators

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming and can improve the performance of exponential integrators. Solving appropriate linear systems of equations in parallel (or computing the inverse of several matrices) and with a proper linear combination of the results, allows us to obtain new high order approximations to the desired functions of matrices. An error analysis to obtain forward and backward error bounds is presented. The coefficients of each method, which depends on the number of processors, can be adjusted to improve the accuracy, the stability or to reduce the round off errors of the methods. We illustrate this procedure by explicitly constructing some methods which are then tested on several numerical examples.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.