论文标题
双重伯恩斯坦多项式的快速准确评估
Fast and accurate evaluation of dual Bernstein polynomials
论文作者
论文摘要
双重伯恩斯坦多项式在近似理论，计算数学，数值分析和计算机辅助几何设计中找到了许多应用。在这种情况下，主要问题之一是这些多项式及其线性组合都快速准确地评估。给出了双重伯恩斯坦多项式满足的低阶的新简单复发关系。特别是，已经获得了连接双伯恩斯坦并移动雅各比正交多项式的一阶非复发关系。正确使用后，它允许提出快速，数值高效的算法，以评估所有$ n+1 $ dual Bernstein多项式$ n $的双伯恩斯坦多项式，并使用$ o（n）$计算复杂性。
Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of these polynomials and their linear combinations. New simple recurrence relations of low order satisfied by dual Bernstein polynomials are given. In particular, a first-order non-homogeneous recurrence relation linking dual Bernstein and shifted Jacobi orthogonal polynomials has been obtained. When used properly, it allows to propose fast and numerically efficient algorithms for evaluating all $n+1$ dual Bernstein polynomials of degree $n$ with $O(n)$ computational complexity.
