An improvement and a generalization of Zippel's sparse multivariate polynomial interpolation algorithm

Authors

Michael D. Brazier, University of Texas-Pan American

Date of Award

12-2005

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Science

First Advisor

Dr. Arthur D. Chtcherba

Second Advisor

Dr. Zhixiang Chen

Third Advisor

Dr. Roger Knobel

Abstract

The algorithm most often used for the problem of interpolating sparse multivariate polynomials from their values is Zippel's probabilistic algorithm (1988). The algorithm evaluates the function to be interpolated at a significant number of points, and for many problems of interest processing evaluations dominates the running time. This thesis presents an improvement of Zippel's algorithm, which decreases the number of evaluations needed for an interpolation by using transposed Vandermonde systems for the univariate interpolation step of Zippel's algorithm. The technique also allows a more general form of the algorithm: it becomes possible to interpolate more than one variable within a single stage of Zippel's method.

Comments

Copyright 2005 Michael D. Brazier. All Rights Reserved.

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Granting Institution

University of Texas-Pan American