New differential-recurrence relations for B-spline basis functions are given. Using these relations, a recursive method for finding the Bernstein-B\'{e}zier coefficients of B-spline basis functions over a single knot span is proposed. The algorithm works for any knot sequence and has an asymptotically optimal computational complexity. Numerical experiments show that the new method gives results which preserve a high number of digits when compared to an approach which uses the well-known de Boor-Cox formula.

翻译：本文提出了B样条基函数的新微分-递推关系式。基于这些关系式，我们提出了一种递归方法，用于计算单节点区间上B样条基函数的Bernstein-Bézier系数。该算法适用于任意节点序列，且具有渐近最优的计算复杂度。数值实验表明，与采用经典de Boor-Cox公式的方法相比，新方法所得结果能保持更高精度的有效数字。