Expedited Award for Novel Research: Fast Polynomial Evaluation and Its Applications

本研究旨在寻找多元多项式的有效求值方法，以此作为信号处理的改进。该方法建立在最近开发的用于快速计算单位平方上的二元多项式的Bernstein型的递归的基础上。首先，将双变量的工作扩展到多变量的情况，以便在等步长的点上进行评估。然后尝试将该程序进一步扩展到单位圆上的求值，即不等距的点。如果成功，后一项任务将在许多信号处理任务中提供显著改进。

This research seeks to find efficient methods for evaluation of multivariate polynomials as an improvement in signal processing. The proposed method builds on the recursion very recently developed for the fast computation of the Bernstein form of a bivariate polynomial on the unit square. First, the bivariate work will be extended to the multivariate case for evaluation at equispaced points. Then an attempt will be made to further extend the procedure to evaluation on the unit circle, that is, unequispaced points. If successful, the latter task would provide a significant improvement in many signal processing tasks.