基于满足三项递推关系的多项式的插值系数的高效构造、更新与降阶
Efficient Construction, Update and Downdate Of The Coefficients Of Interpolants Based On Polynomials Satisfying A Three-Term Recurrence Relation
AI总结：
本文提出两种新算法，用于高效计算基于满足三项递推关系的多项式基的插值系数，支持节点增删时的系数更新，并对比了数值稳定性与计算效率。
摘要：
本文考虑了相对于满足三项递推关系的多项式基的插值系数的计算方法。提出了两种新算法：第一种算法增量地构造插值系数，可用于在插值中添加或移除节点时更新系数。第二种算法通过迭代分解类Vandermonde矩阵来构造插值系数，不能用于更新或降阶插值，但比第一种算法数值稳定性更高，并且在相同节点集上计算多个插值系数时效率更高。
英文摘要：
In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the interpolation incrementally and can be used to update the coefficients whenever a nodes is added to or removed from the interpolation. The second algorithm, which constructs the interpolation coefficients by decomposing the Vandermonde-like matrix iteratively, can not be used to update or downdate an interpolation, yet is more numerically stable than the first algorithm and is more efficient when the coefficients of multiple interpolations are to be computed over the same set of nodes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
