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中文摘要：
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．
英文摘要：
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.
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