|
| This Article | ||
| ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
| | ||
| Search | ||
| ||
| ASCII Text | x | ||
| Zeljko Zilic, Zvonko G. Vranesic, "A Deterministic Multivariate Interpolation Algorithm for Small Finite Fields," IEEE Transactions on Computers, vol. 51, no. 9, pp. 1100-1105, September, 2002. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.2002.1032628, author = {Zeljko Zilic and Zvonko G. Vranesic}, title = {A Deterministic Multivariate Interpolation Algorithm for Small Finite Fields}, journal ={IEEE Transactions on Computers}, volume = {51}, number = {9}, issn = {0018-9340}, year = {2002}, pages = {1100-1105}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2002.1032628}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - A Deterministic Multivariate Interpolation Algorithm for Small Finite Fields IS - 9 SN - 0018-9340 SP1100 EP1105 EPD - 1100-1105 A1 - Zeljko Zilic, A1 - Zvonko G. Vranesic, PY - 2002 KW - Multivariate interpolation KW - finite fields KW - Vandermonde matrices KW - Reed-Muller transform. VL - 51 JA - IEEE Transactions on Computers ER - | |||
Abstract—We present a new multivariate interpolation algorithm over arbitrary fields which is primarily suited for small finite fields. Given function values at arbitrary
[1] Z. Zilic and Z.G. Vranesic, “A Multiple Valued Reed-Muller Transform for Incompletely Specified Functions,” IEEE Trans. Computers, vol. 44, no. 8, pp. 1012-1020, Aug. 1995.
[2] C. de Boor and A. Ron, “Computational Aspects of Polynomial Interpolation in Several Variables,” Math. Computation, vol. 58, pp. 705-727, 1992.
[3] V. Guruswami and M. Sudan, “Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes,” Proc. Symp. Discrete Algorithms, pp. 108-117, Nov. 1998.
[4] T. Damarla and M.G. Karpovsky, “Reed-Muller Spectral Techniques for Fault Detection,” IEEE Trans. Computers, vol. 38, pp. 788-797, 1989.
[5] R.E. Schapire and L.M. Sellie, “Learning Sparse Multivariate Polynomials over a Field with Queries and Counterexamples,” Proc. Symp. Computational Learning Theory (COLT '93), pp. 17-26, May 1993.
[6] D.H. Green, “Reed-Muller Expansions of Incompletely Specified Functions,” IEE Proc., Part E, vol. 134, no. 5, pp. 228-236, Sept. 1987.
[7] A. Zakrevskij, “Minimum Polynomial Implementations of Systems of Incompletely Specified Boolean Functions,” Proc. Second Workshop Applications of the Reed-Muller Expansions in Circuit Design, Aug. 1995.
[8] W.G. Schneeweiss, “On the Polynomial Form of Boolean Functions: Derivations and Applications,” IEEE Trans. Computers, vol. 47, no. 2, pp. 217-221, Feb. 1998.
[9] K. Radecka and Z. Zilic, “Using Arithmetic Transform for Verification of Datapath Circuits via Error Modeling,” Proc. VLSI Test Symp. (VTS 2000), pp. 271-277, 2000.
[10] Z. Zilic and K. Radecka, “Don't Care Minimization by Interpolation,” Proc. Int'l Workshop Logic Synthesis (IWLS '98), pp. 353-356, May 1998.
[11] D. Bojanov, H.A. Hakopian, and A.A. Sahakian, Spline Functions and Multivariate Interpolations. Kluwer Academic, 1993.
[12] A. Dur and J. Grabmeier, “Applying Coding Theory to Sparse Interpolation,” SIAM J. Computing, vol. 22, no. 4, pp. 695-703, Aug. 1993.
[13] D.Y. Grigoriev, M. Karpinski, and M.F. Singer, “Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields,” SIAM J. Computing, vol. 19, no. 6, pp. 1059-1063, Dec. 1990.
[14] M. Ben-Or and P. Tiwari, “A Deterministic Algorithm for Sparse Multivariate Polynomial Interpolation,” Proc. 20th Symp. Theory of Computing, pp. 301-309, Apr. 1988.
[15] R.M. Roth and G.M. Benedek, “Interpolation and Approximation of Sparse Multivariate Polynomials over GF(2),” SIAM J. Computing, vol. 20, no. 2, pp. 291-314, Apr. 1991.
[16] E. Kaltofen, W.-S. Lee, and A.A. Lobo, “Early Termination in Ben-Or/Tiwari Sparse Interpolation and a Hybrid of Zippel's Algorithm,” Proc. Int'l Symp. Symbolic and Algebraic Computing, pp. 192-201, 2000.
[17] K. Werther, “The Complexities of Sparse Polynomial Interpolation over Finite Fields,” Applicable Algebra in Eng., Comm., and Computing, vol. 5, pp. 192-201, 1994.
[18] M. Clausen, A. Dress, J. Grebmeier, and M. Karpinski, “On Zero-Testing and Interpolation of k-Sparse Polynomials over Finite Fields,” Theoretical Computer Science, vol. 84, no. 2, pp. 151-164, Jan. 1991.
[19] R. Zippel, “Interpolating Polynomials from Their Values,” J. Symbolic Computation, vol. 9, pp. 375-403, Mar. 1990.
[20] T. Sauer, “Polynomial Interpolation of Minimal Degree,” Numerische Mathematik, vol. 78, pp. 59-85, 1997.
[21] D. Knuth, The Art of Computer Programming, Vol. 2, Addison-Wesley, Reading, Mass., 1998.
[22] J. von zur Gathen and G. Juergen, Modern Computer Algebra. Cambridge Univ. Press, 1999.
[23] Z. Zilic, “Towards Spectral Synthesis: Field Expansions for Partial Functions and Logic Modules for FPGAs,” PhD dissertation, Dept. of Electrical and Computer Eng., Univ. of Toronto, Jan. 1997.
[24] Z. Zilic and Z. Vranesic, “Parallel Sparse Finite Field Interpolation,” Proc. First IEEE Workshop Randomized Parallel Computing, pp. 9-16, Apr. 1996.

