样条最佳插值结点的非线性规划算法

§1.问题的提出 1]研究了二阶算子样条最佳插值结点的特征.对于少数几个函数,利用特征定理精确求出了其最佳插值结点.但是,如1]中指出,对于绝大多数函数,要精确求出其最佳插值结点,是相当困难的.因此,设计相应的数值求解方法,对于实际应用是很有必要的.

NONLINEAR PROGRAMMING ALGORITHMS FOR THE BEST INTERPOLATION KNOTS OF A SPLINE

This paper reduces the problem of finding the best interpolation knots of a spline to anequivalent nonlinear programming problem which is easy to be discussed. This result allows us todesign two iterative algorithms for finding the best interpolation knots of an operator splineof order two. The convergence of the coordinate search algorithm is proved and a numericalexample is also given.