摘要
研究从数值积分公式的代数精度概念出发,通过直接对涉及的非线性代数方程组进行分析,即无需用到正交多项式的单根特性,获得了求积系数ai的计算公式和Gauss求积公式存在性及其构造,并以推论的方式获得了正交多项式的单根特性.
Abstract
In this paper,we will,from the concept of algebraic precision of the numerical integral formula,by directly analyzing the involved nonlinear algebraic equations,without using the single-root feature of orthogonal polynomials,obtain the calculation formula of the coefficients ai of Gaussian integral formula,at the same time,obtain the existence and structure of the Gauss formula of numerical quadrature,subsequently,the single-root feature of orthogonal polynomial is obtained through the inference.
基金项目
安徽省高校优秀青年人才支持计划项目(gxyq2020098)
维普
万方数据