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

本研究旨在寻找评估多元多项式的有效方法，以改善信号处理。所提出的方法建立在递归的基础上，递归是最近为单位平方上二元多项式的Bernstein形式的快速计算而发展起来的。首先，二元的工作将扩展到多元的情况下，以评估在均衡点。然后，尝试将该程序进一步扩展到单位圆上的评估，即不均匀点。如果成功，后一项任务将为许多信号处理任务提供显着改进。

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.