【摘要】 将Th iele型插值连分式与二元Newton插值多项式结合起来构造三元有理函数,通过引入三元混合差商和倒差商建立了三元有理插值的递推算法、特征定理,给出了相应的证明,并通过数值例子验证了算法的有效性。三元有理插值在几何造型、图像处理、计算机辅助设计等领域都有直接的应用。更多还原

【Abstract】 Tri-variate rational function is structured by incorporating Thiele’s branched continued fraction in bivariate Newton’s interpolation polynomials.By defining tri-variate mixed difference and inverse difference,tri-variate rational interpolating algorithm is built,and interpolating characteristical theorem and its proof are given.A numerical example is presented to illustrate the efficiency of this algorithm.Tri-variate rational interpolating has direct application in geometrical modeling,image processing and CAGD,etc.更多还原