结合二元Thiele 型插值分叉连分式和牛顿插值多项式, 通过引入混合偏差商构造三元有理插值, 进一步给出其特征定理和误差估计, 最后给出数值算例.
The bivariate Thiele-type interpolating branched continued fractions and Newton interpolation polynomials are combined. By introducing the so-called blending partial differences, a triple rational interpolation scheme is obtained. The characteristic theorem and error estimation are presented. Finally, an example is given.
[1] Wang R H. Numerical rational approximation [M]. Shanghai: Science and Technology Press, 1980: 1-181.
[2] Cui R R, Gu C Q, A new algorithm to approximate bivariate matrix function via Newton-Thiele type formula [J]. J Appl Math, 2013: 642818.
[3] Gu C Q, Zhang Y. An osculatory rational interpolation method of model reduction in linear system [J]. Journal of Shanghai University: English Edition, 2007, 11(4): 365-369.
[4] Gu C Q, Wang J B. Werner-type matrix valued rational interpolation and its recurrence algorithms [J]. Journal of Shanghai University: English Edition, 2004, 8(4): 425-438.
[5] Zhao Q J, Liang X K. Triple blending rational interpolants [J]. Journal of Hefei University of Technology, 2001, 24: 277-281.
[6] Zhang G F. Bivariate Thiele-type branched continued fraction and general order Padé approximation [J]. Appl Math Lett, 1989, 2: 199-202.
[7] Tan J Q, Fang Y. Newton-Thieles rational interpolants [J]. Numer Algorithms, 2000, 24: 141-157.
