A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
Modular rational sparse multivariate polynomial interpolation
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Improved Sparse Multivariate Polynomial Interpolation Algorithms
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Modern Computer Algebra
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Algorithms for the non-monic case of the sparse modular GCD algorithm
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A sparse modular GCD algorithm for polynomials over algebraic function fields
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Symbolic-numeric sparse interpolation of multivariate polynomials
Journal of Symbolic Computation
On sparse interpolation over finite fields
ACM Communications in Computer Algebra
Sparse interpolation of multivariate rational functions
Theoretical Computer Science
Diversification improves interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
| Hi-index | 0.00 |
We present a probabilistic algorithm to interpolate a sparse multivariate polynomial over a finite field, represented with a black box. Our algorithm modifies the algorithm of Ben-Or and Tiwari from 1988 for interpolating polynomials over rings with characteristic zero to characteristic p by doing additional probes. To interpolate a polynomial in n variables with t non-zero terms, Zippel's (1990) algorithm interpolates one variable at a time using O(ndt) probes to the black box where d bounds the degree of the polynomial. Our new algorithm does O(nt) probes. It interpolates each variable independently using O(t) probes which allows us to parallelize the main loop giving an advantage over Zippel's algorithm. We have implemented both Zippel's algorithm and the new algorithm in C and we have done a parallel implementation of our algorithm using Cilk [2]. In the paper we provide benchmarks comparing the number of probes our algorithm does with both Zippel's algorithm and Kaltofen and Lee's hybrid of the Zippel and Ben-Or/Tiwari algorithms.