论文标题
朝向非线性正交公式
Towards non-linear quadrature formulae
论文作者
论文摘要
在观察到表格$ f（x）=λ\ mathrm {e}^{αx} $的指数函数的积分的提示中，我们研究了准确地整合通过缩放或使用非线性概括的Quader pransinations缩放函数产生的函数系族的可能性。本文的主要结果是，可以为广泛的功能明确构建此类公式，并且具有与基于相同节点的牛顿 - 汤匙公式相同的准确性。我们还展示了牛顿 - 托尔公式如何作为我们的一般形式主义的线性案例出现，并在指数分析的Padé-Laplace方法中证明了非线性公式的有用性。
Prompted by an observation about the integral of exponential functions of the form $f(x)=λ\mathrm{e}^{αx}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by affine transformations of the argument using nonlinear generalizations of quadrature formulae. The main result of this paper is that such formulae can be explicitly constructed for a wide class of functions, and have the same accuracy as Newton-Cotes formulae based on the same nodes. We also show how Newton-Cotes formulae emerge as the linear case of our general formalism, and demonstrate the usefulness of the nonlinear formulae in the context of the Padé-Laplace method of exponential analysis.
