4阶均匀代数三角样条空间的拟Legendre基

摘要

In order to develop the theory of orthogonal basis for algebraic-trigonometric spline space, a novel approach is presented to construct an orthogonal basis for the uniform four-order algebraic trigonometric spline space.Based on the C-B spline functions of order six, a set of auxiliary functions is constructed.And the proposed orthogonal splines are given as the second-order derivatives of these auxiliary functions.This orthogonal basis is also called Legendre-like basis.The result of the practical examples shows that using this basis can simplify inner product computation and facilitate solving least-squares approximation.%为解决代数三角样条空间上正交基的理论问题,提出了4阶均匀代数三角样条空间上构造正交基的方法.该方法利用6阶C-B样条基函数构造一组辅助函数,并以这组辅助函数的二阶导数形式定义样条空间上的一组正交基,称为拟Legendre基.实例结果表明,使用这组正交基可以简化内积计算,便于最佳平方逼近问题求解.