In Farouki et al , 2003, Legendre-weighted orthogonal polynomials P n , r ( u , v , w ) , r = 0 , 1 , … , n , n ≥ 0 on the triangular domain T = { ( u , v , w ) : u , v , w ≥ 0 , u + v + w = 1 } are constructed, where u , v , w are the barycentric coordinates. Unfortunately, evaluating the explicit formulas requires many operations and is not very practical from an algorithmic point of view. Hence, there is a need for a more efficient alternative. A very convenient method for computing orthogonal polynomials is based on recurrence relations. Such recurrence relations are described in this paper for the triangular orthogonal polynomials, providing a simple and fast algorithm for their evaluation.
展开▼
机译：在Farouki等人的2003年中，三角域T = {（（u，v，w）上的Legendre加权正交多项式P n，r（u，v，w），r = 0，1，…，n，n≥0 ）：构造u，v，w≥0，u + v + w = 1}，其中u，v，w是重心坐标。不幸的是，评估显式公式需要许多操作，从算法的角度来看不是很实际。因此，需要一种更有效的替代方案。计算递归多项式的一种非常方便的方法是基于递归关系。本文针对三角正交多项式描述了此类递归关系，提供了一种简单快速的求值算法。
展开▼
