| 一种有理插值型求积公式的收敛性 |
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| 引用本文： | 周志强. 一种有理插值型求积公式的收敛性[J]. 大学数学, 2008, 24(5) |
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| 作者姓名： | 周志强 |
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| 作者单位： | 怀化学院,数学系,湖南,怀化,418008 |
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| 基金项目： | 湖南省教育厅科研基金资助项目 |
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| 摘 要： | 构造一种有理插值型求积公式,证明其收敛性,并给出数值计算实例.该方法推广了Sloan和Smith等人的结果.
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| 关 键 词： | 正交多项式 权函数 插值型求积公式 |
On the Convergence of Rational Interpolatory Quadrature Formulas |
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| ZHOU Zhi-qiang. On the Convergence of Rational Interpolatory Quadrature Formulas[J]. College Mathematics, 2008, 24(5) |
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| Authors: | ZHOU Zhi-qiang |
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| Abstract: | Let ω be a L1 integrable function on [-1,1] and denote Iω(f)=∫1-1ω(x)f(x)dx, where f(x) is any bounded integrable function with respect to the weight function ω. In this paper, we consider rational interpolatory quadrature formulas (RIQFs) for Rn={p(x)Πn(x),p∈Pn-1}, and study the convergence of the RIQFs. At the same time, numerical examples are given, that support the theory developed in this paper. |
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| Keywords: | orthogonal polynomial RIQFs weight functions |
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