Linear and nonlinear evolution equations have been formulated to address problems in various fields of science and technology. Recently, methods using an exponential integrator for solving evolution equations, where matrix functions must be computed repeatedly, have been investigated and refined. In this paper, we propose a new method for computing these matrix functions which is called an inexact rational Krylov method. This is a more efficient version of the rational Krylov method with appropriate shifts, which was proposed by Hashimoto and Nodera (ANZIAM J 58:C149–C161, 2016). The advantage of the inexact rational Krylov method is that it computes linear equations that appear in the rational Krylov method efficiently while guaranteeing the accuracy of the final solution.

中文翻译：

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演化方程的非精确有理 Krylov 方法

已经制定了线性和非线性演化方程来解决各个科学和技术领域的问题。最近，已经研究和改进了使用指数积分器求解演化方程的方法，其中矩阵函数必须重复计算。在本文中，我们提出了一种计算这些矩阵函数的新方法，称为不精确有理 Krylov 方法。这是 Hashimoto 和 Nodera (ANZIAM J 58:C149–C161, 2016) 提出的具有适当移位的有理 Krylov 方法的更有效版本。不精确有理 Krylov 方法的优点是它可以有效地计算出现在有理 Krylov 方法中的线性方程，同时保证最终解的准确性。