A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
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IEEE Transactions on Computers
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Journal of Symbolic Computation - Special issue on computational algebraic complexity
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SIAM Journal on Computing
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Theoretical Computer Science
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SIAM Journal on Computing
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COLT '93 Proceedings of the sixth annual conference on Computational learning theory
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IEEE Transactions on Computers
Modern computer algebra
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ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
A Multiple-Valued Reed-Muller Transform for Incompletely Specified Functions
IEEE Transactions on Computers
Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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VTS '00 Proceedings of the 18th IEEE VLSI Test Symposium
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Towards spectral synthesis: field expansions for partial functions and logic modules for fgpas
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IEEE Transactions on Computers
An efficient technique for synthesis and optimization of polynomials in GF(2m)
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
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IEEE Transactions on Computers
Reconfigurable hardware implementation of a multivariate polynomial interpolation algorithm
International Journal of Reconfigurable Computing - Special issue on selected papers from ReconFig 2009 International conference on reconfigurable computing and FPGAs (ReconFig 2009)
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We present a new multivariate interpolation algorithm over arbitrary fields which is primarily suited for small finite fields. Given function values at arbitrary $\big. t\bigr.$ points, we show that it is possible to find an n-variable interpolating polynomial with at most $\big. t\bigr.$ terms, using the number of field operations that is polynomial in $\big. t\bigr.$ and $\big. n\bigr.$. The algorithm exploits the structure of the multivariate generalized Vandermonde matrix associated with the problem. Relative to the univariate interpolation, only the minimal degree selection of terms cannot be guaranteed and several term selection heuristics are investigated toward obtaining low-degree polynomials. The algorithms were applied to obtain Reed-Muller and related transforms for incompletely specified functions.