| 摘要: |
| 利利用正交多项式的三项递推关系，定义一个新的 次正交多项式,用它的 个零点作为求积节点,利用分离奇点的方法，构造Cauchy主值积分的内插型反Gauss求积公式.证明求积公式的代数精度至少为 .当被积函数为次数小于或等于 的多项式时, Cauchy主值积分 个节点的Gauss求积公式误差与 个节点的反Gauss求积公式误差绝对值相等,符号相反.对带Legendre权和Chebyshev权的Cauchy主值积分的反Gauss求积公式进行了数值实验，实验中实例的误差数值积分图像表明，实验结果与理论分析相符. |
| 关键词: 正交多项式 Cauchy主值积分 反Gauss求积公式 代数精度 |
| DOI： |
| 分类号:024 |
| 基金项目:湖北省教育厅科研计划项目 |
|
| Anti-Gauss quadrature for Cauchy principal value integrals |
|
Ding Yong
|
| Abstract: |
| A new orthogonal polynomial was defined by using the three-term recurrence relation for orthogonal polynomials, and an interpolatory --point anti-Gauss quadrature formulae for Cauchy principal value integrals were constructed by use of the method of separating singularity, which the quadrature nodes are the zeros of the new orthogonal polynomial . We show that the quadrature formula has at least degree algebraic accuracy , and an error of the --point anti-Gauss quadrature formulae equal in magnitude but of opposite sign to that of the --point Gauss quadrature formula when integrand function is the polynomials of degree up to . The anti-Gaussian quadrature formulae for Cauchy principal value integrals with Legendre and Chebyshev weight functions are numerical tested. According to the error results and numerical integral images of the examples in the experiments, the experimental results are according with our theoretical analysis. |
| Key words: orthogonal polynomial Cauchy principal value integrals anti-Gauss quadrature formulae algebraic accuracy |
