| 摘要: |
| 基于高斯-勒让德求积公式余项,给出一种新的数值积分校正公式.该校正公式相比原高斯型求积公式可提高四阶代数精度,即n点校正公式的代数精度至少达2n+3,而且数值算例表明,该校正公式的数值精度明显优于原高斯型求积公式和其他已知的计算结果. |
| 关键词: 高斯积分 代数精度 校正公式 数值算例 |
| DOI：10.13656/j.cnki.gxkx.20140430.005 |
| 投稿时间：2013-09-20修订日期：2013-10-15 |
| 基金项目:广西民族大学研究生创新项目(gxun-chx2012099),广西高校科研基金项目(2013YB076)资助。 |
|
| The New Correction Formulas of Gauss Quadrature |
|
TAN Yun-long, HUANG Jing-pin
|
| (College of Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China) |
| Abstract: |
| Based on the remainder of Gauss-Legendre quadrature formula, a new correction formula for numerical integral is given.And it is proved that the correction formula can improve four-order algebraic accuracy compared with traditional Gauss integral formula, that is, the algebraic accuracy of n-point correction formula to be at least 2n+3.Numerical examples show that the correction formulas have higher accuracy than the traditional Gauss integral and the results obtained from other relevant literature. |
| Key words: Gauss integral algebraic accuracy correction formula numerical example |
