论文信息 - A deterministic algorithm for sparse multivariate polynomial interpolation - 字舞流文

A deterministic algorithm for sparse multivariate polynomial interpolation

An efficient deterministic polynomial time algorithm is developed for the sparse polynomial interpolation problem. The number of evaluations needed by this algorithm is very small. The algorithm also has a simple NC implementation.

Michael Ben-Or | Prasoon Tiwari | M. Ben-Or | Prasoon Tiwari

[1] E. Berlekamp. Factoring polynomials over large finite fields* , 1971, SYMSAC '71.

[2] R. Evans,et al. Generalized Vandermonde determinants and roots of unity of prime order , 1976 .

[3] Richard Zippel,et al. Probabilistic algorithms for sparse polynomials , 1979, EUROSAM.

[4] Jacob T. Schwartz,et al. Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[5] R. Blahut. Theory and practice of error control codes , 1983 .

[6] Rüdiger Loos. Computing Rational Zeros of Integral Polynomials by p-adic Expansion , 1983, SIAM J. Comput..

[7] Joachim von zur Gathen. Parallel Powering , 1984, FOCS.

[8] Leonard M. Adleman,et al. Finding irreducible polynomials over finite fields , 1986, STOC '86.

[9] J.L. Massey,et al. Theory and practice of error control codes , 1986, Proceedings of the IEEE.

[10] Marek Karpinski,et al. The matching problem for bipartite graphs with polynomially bounded permanents is in NC , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[11] Erich Kaltofen,et al. Factorization of Polynomials Given by Straight-Line Programs , 1989, Adv. Comput. Res..

[12] Richard Zippel,et al. Interpolating Polynomials from Their Values , 1990, J. Symb. Comput..