| 基于Thiele型连分式的数值积分 |
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| 引用本文： | 钱江,吴云标.基于Thiele型连分式的数值积分[J].数学的实践与认识,2014(10). |
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| 作者姓名： | 钱江 吴云标 |
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| 作者单位： | 河海大学理学院;河海大学水文水资源与水利工程科学国家重点实验室;河海大学文天学院基础部; |
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| 基金项目： | 中央高校业务费资助项目;河海大学博士后科研基金(2016-412051);安徽省级项目大学数学课程教学团队(2002);河海大学文天学院重点教学研究项目(Z1201206) |
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| 摘 要： | 基于Thiele型连分式构造求积公式,这类求积公式能再生由Thiele型连分式前三项渐近式的线性组合所表示的任意有理函数,接着算出求积余项,并推导出分母在给定区间上无零点的充分条件.更进一步,通过等分给定区间,构造相应的复化求积公式,并算出求积余项.研究表明,在若干条件满足的前提下,复化求积公式序列能一致收敛于积分真值,一些数值算例说明了这一点.
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| 关 键 词： | Thiele型连分式 数值积分 复化求积公式 求积余项 逆差商 |
Numerical Integration based on Thiele Type Continued Fractions |
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| Abstract: | In this paper,based on Thiele type continued fractions,the cubature formula is constructed,which can reproduce any rational function in the form of the linear combination of the former three convergents for the Thiele type continued fraction.Then the residual item of cubature is worked out,and the sufficient condition is derived to ensure no zero for the denominator existing in the interval.Moreover,the corresponding composite cubature formula is developed with the interval partitioned equally.And the the residual item of cubature is determined as well.In some cases,the composite cubature formula sequence can converge to the integral uniformly as n→∞,which is valid for some special integral. |
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| Keywords: | Thiele type Continued fraction Numerical integration composite cubature formula residual item of cubature inverse divided difference |
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