The efficient evaluation of multivariate polynomials at many points is an important operation for polynomial system solving. Kedlaya and Umans have recently devised a theoretically efficient algorithm for this task when the coefficients are integers or when they lie in a finite field. In this paper, we assume that the set of points where we need to evaluate is fixed and “sufficiently generic”. Under these restrictions, we present a quasi-optimal algorithm for multi-point evaluation over general fields. We also present a quasi-optimal algorithm for the opposite interpolation task.

中文翻译：

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快速摊销多点评估

在许多点上对多元多项式进行有效求值是多项式系统求解的重要操作。Kedlaya 和 Umans 最近为这项任务设计了一种理论上有效的算法，当系数是整数或当它们位于有限域中时。在本文中，我们假设需要评估的点集是固定的且“足够通用”。在这些限制下，我们提出了一种用于一般领域多点评估的准最优算法。我们还提出了一种用于相反插值任务的准最优算法。