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

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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.