三角网格上的矩阵值混合有理插值算法  

Matrix valued blending rational interpolation algorithm on the triangular grid

作　　者：唐烁[1] 郑涛[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2010年第11期1753-1756,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省自然科学基金资助项目(070416227);安徽省教育厅重点基金资助项目(KJ2008A027)

摘　　要：文章利用Samelson型矩阵广义逆,将Stieltjes型分叉连分式与Thiele型矩阵多项式结合起来,通过定义矩阵的差商和混合逆差商,建立递推算法,构造了三角网格上的Stieltjes-Thiele型矩阵值混合有理插值公式,该算法满足有理插值问题所给的插值条件;并给出了特征定理及其证明,最后用数值算例验证了插值定理的有效性。In this paper,by defining the matrix partial difference quotient and the blending inverse difference quotient,and by means of Samelson-type generalized inverse of matrixes,the Stieltjes-Thiele matrix valued blending rational interpolation formula is constructed on the triangular grids via the recursive algorithm based on the combination of Thiele-type polynomials and the Stieltjes-type continued fractions.The given interpolating conditions are satisfied by this algorithm,and the characteristic theorem and its demonstration are given.A numerical example is presented to illustrate the effectiveness of the interpolating theorem.

关 键 词：有理插值 Samelson广义逆 矩阵连分式 

分 类 号：O241.3[理学—计算数学]