Theses and Dissertations - UTB/UTPA
An improvement and a generalization of Zippel's sparse multivariate polynomial interpolation algorithm
Date of Award
Master of Science (MS)
Dr. Arthur D. Chtcherba
Dr. Zhixiang Chen
Dr. Roger Knobel
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.
University of Texas-Pan American
Copyright 2005 Michael D. Brazier. All Rights Reserved.