Stieltjes-Thiele型二元混合有理插值

Stieltjes-Thiele Blending Rational Interpolation

文章基于Stieltjes型连分式,在下三角形网格上构造了一种Stieltjes-Thiele型二元混合有理插值函数.通过定义混合逆差商,由Stieltjes型和Thiele型连分式的递推性质,证明该有理插值函数满足插值性,且给出了该插值函数的特征性和误差估计.最后,通过数值算例验证了该算法的有效性.

Based on the Stiehjes type continuous fraction, a kind of Stiehjes-Thiele binary mixed rational in-terpolation is constructed on the lower triangular mesh. By defining the mixed inverse diffrence quotient, and u-sing the recursive nature of Stieltjes-type and Thiele-type continuous fraction, the rational interpolation function sat- isfies the given interpolation property, and the characterization and error of the interpolated function are obtained. Finally, a numerical example is given to illustrate the effectiveness of algorithm.