摘要
首先利用Newton-Pade表中部分序列推导出连分式,提出逆差商算法,算出关于高阶导数与高阶差商的连分式插值余项.接着,构造基于此类连分式的有理求积公式与相应的复化求积公式,算出相应的求积余项,研究表明,在一定条件下,求积公式序列一致收敛于积分真值.然后,为保证连分式计算顺利进行,研究连分式分母非0的充分条件.最后,若干数值算例表明,对某些函数采用新提出的复化有理求积公式计算数值积分,所得结果优于采用Simpson公式.
In this paper, the convergents of the continued fractions are derived from power series as some particular subsequences of the Newton-Pade table with inverse divided difference algorithm presented, and two kinds of error-estimated representation are given in term of derivatives and divided difference with high order. Moreover, based on the continued fractions, the cubature formulaes and the corresponding composite ones are constructed, which converge to the real value of the integration uniformly. Furthermore, the corresponding error estimation is worked out. For the sake of ensuring the smooth computation of the continued fractions, the sufficient condition is discussed when the denominators of the convergents axe not equal to zero. Finally, numerical examples show that the new composite rational cubature formulae is much advantageous over the composite Simpson scheme for some special functions.
出处
《数学的实践与认识》
北大核心
2017年第4期194-208,共15页
Mathematics in Practice and Theory
基金
国家自然科学基金天元专项基金(11426086)
中央高校业务费项目(2016B08714)
江苏省自然科学基金青年基金项目(BK20160853)
关键词
Newton-Pade逼近
连分式
逆差商
数值积分
复化有理求积公式
newton-pade approximation
continued fraction
inverse divided difference
nu- merical integration
composite rational cubature formulae
