| 插值型求积公式的代数精度 |
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| 引用本文： | 王伟,严志丹,胡汉涛.插值型求积公式的代数精度[J].大学数学,2010,26(5). |
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| 作者姓名： | 王伟 严志丹 胡汉涛 |
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| 基金项目： | 塔里木大学质量工程项目 |
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| 摘 要： | 借助于勒让德多项式的零点性质,证明了N阶插值型求积公式的代数精度可取N到2 N+1之间的任意整数值,计算得到了两点插值型求积公式的代数精度与求积节点位置的关系.简化了1]中关于3次代数精度的条件的讨论.
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| 关 键 词： | 插值型求积公式 代数精度 勒让德多项式 |
Algebraic Precision of Interpolatory Quadrature Formulae |
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| WANG Wei,YAN Zhi-dan,HU Han-tao.Algebraic Precision of Interpolatory Quadrature Formulae[J].College Mathematics,2010,26(5). |
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| Authors: | WANG Wei YAN Zhi-dan HU Han-tao |
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| Abstract: | We prove that the algebraic precision of a(N+1)-point interpolatory quadraure formula can take any integer value from Nto 2 N+1by the roots property of Legendre polynomials.We give a complete answer to the relationship between algebraic precision and positions of nodes when N=1.As a by-product,we present a simple proof of the condition when the degree of precision of a quadrature formula is 3discussed in1]. |
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| Keywords: | interpolatory quadrature formula algebraic precision Legendre polynomial |
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