Early termination in sparse interpolation algorithms

Authors:
Erich Kaltofen;Wen-shin Lee
Affiliations:
Department of Mathematics, North Carolina State University, Raleigh, NC;School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Venue:
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Year:
2003

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Abstract

A probabilistic strategy, early termination, enables different interpolation algorithms to adapt to the degree or the number of terms in the target polynomial when neither is supplied in the input. In addition to dense algorithms, we implement this strategy in sparse interpolation algorithms. Based on early termination, racing algorithms execute simultaneously dense and sparse algorithms. The racing algorithms can be embedded as the univariate interpolation substep within Zippel's multivariate method. In addition, we experimentally verify some heuristics of early termination, which make use of thresholds and post-verification.