用有理逼近计算$ϕ$ -函数的倒数
Computing the Reciprocal of a $ϕ$-function by Rational Approximation
摘要：
在本文中，我们介绍了一个$ϕ$ -函数的倒数的有理逼近的家庭涉及某些线性微分方程的显式解决方案，以及在流形上发展的积分计划。推导和属性，这一家庭的近似适用于标量和矩阵参数。此外，我们表明，这些近似计算的矩阵函数表现出衰减性能相媲美的最佳现有的理论界。数值例子突出了建议的有理逼近的好处w.r.t.~经典的泰勒多项式和其他有理函数。
英文摘要：
In this paper we introduce a family of rational approximations of the reciprocal of a $ϕ$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The derivation and properties of this family of approximations applied to scalar and matrix arguments are presented. Moreover, we show that the matrix functions computed by these approximations exhibit decaying properties comparable to the best existing theoretical bounds. Numerical examples highlight the benefits of the proposed rational approximations w.r.t.~the classical Taylor polynomials and other rational functions.
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