Thiele重心型矩阵值混合有理插值算法

Thiele-barycentric Type Matrix-valued Blending Rational Interpolant Algorithm

利用Samelson型矩阵广义逆,构造了一种基于Thiele型连分式插值与重心有理插值的相结合的二元矩阵值混合有理插值格式,这种新的混合矩阵值有理插值函数继承了连分式插值和重心插值的优点,它的表达式简单,计算方便,数值稳定性好.该算法满足有理插值问题所给的插值条件,同时给出了误差估计分析.最后用数值算例验证了插值算法的有效性.

By use of Samelson type generalized inverse of matrixs, a model of the thiele-barycentric type matrix- valued bivariate blending rational interpolant algorithm was constructed on the rectangular grids, which based on the combination of thiele-type continued fraction interpolation and barycentric rational interpolantion. This new blending matrix-valued rational interpolation inherited the advantages of the continued fraction interpolation and the barycentric interpolation, also it had simple expression, numerical stability and was easy to calculate . The algorithm satisfied the given interpolating conditions and then the error estimation analysis was given out. In the end, a numerical example was presented to illustrate the efficiency of this algorithm.