二次基函数的构造及其应用

THE CONSTRUCTION AND APPLICATIONS OF QUADRATIC BASIS FUNCTIONS

本文构造了具有二次代数精度的基函数，这些基函数无论在计算方面还是在应用方面都比Ｅ．Ｌ．Ｗａｃｈｓｐｒｅｓｓ所建立的方便．利用这些基函数，得到了三角剖分下插值多元样条ｕ（ｘ，ｙ）∈Ｓ（△，Ｄ）存在的充要条件，并以数值便阐明了求解插值多元作条空间的维数问题．

Quadratic hasis functions are constructed which are shown to be more convenient for computations and applications than those E. L. Wachspress. These basis functions can be used to ddtermine the necessary and sufficient conditions for the existence of interpolating multivariate splines in. triangulation and further to solve the. dimension problems of the spaces,which is illustrated by a numerical example where interpolating bivariate spine u(x,y) in the space S(A,D) is treated.