摘要
一元样条大致从以下三个方向上发展起来的:一元截断多项式样条;一元B-样条;一元分片多项式样条。二元样条的研究已取得了不少进展,文[2]可视为一元截断多项式样条向二元截断多项式样条推广的奠基性的工作,文[3]又讨论了二元B样条的构造方面的进展,但一元分片多项式样条的构造方法如何推广到二元样条上来,几乎没有见到什么工作。我们曾在文[4]中作过一点努力。
We consider bivariate piecewise cubic polynomial spline. Theorem 1 constructedit's expression on the rectangle R as (R). Theorem 2-5 gave four methods of spline interpolation. They show the close connect between bivariate and one variate spline. Using the data that is produced to constructe one variate cubic spline on each partition line, we write the expression of bivariate piecewise cubic interpolation spline at once. When f(x, y)∈C^4(R), approximantion degree of the interpolation splines that theorem 2-5 give is 4, as same its one variate spline.
出处
《应用数学与计算数学学报》
1992年第2期1-12,共12页
Communication on Applied Mathematics and Computation
