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Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm

Erich Kaltofen, Wen-shin Lee, Austin A. Lobo
2000 Proceedings of the 2000 international symposium on Symbolic and algebraic computation symbolic and algebraic computation - ISSAC '00  
Davenport and two anonymous referees for their comments. Note: many of the authors' publications cited below are accessible through links in their Internet homepages listed under the title.  ...  Thus is the genesis of the hybrid Ben-Or/Tiwari/Zippel algorithm.  ...  Therefore, we revert back to Zippel's algorithm, but now implement each univariate polynomial interpolation as the early termination version of the Ben-Or/Tiwari algorithm.  ... 
doi:10.1145/345542.345629 dblp:conf/issac/KaltofenLL00 fatcat:eens6ou3cbbibf7tnezoc3tt64

Early termination in sparse interpolation algorithms

Erich Kaltofen, Wen-shin Lee
2003 Journal of symbolic computation  
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.  ...  In addition, we experimentally verify some heuristics of early termination, which make use of thresholds and post-verification. where n is the number of columns in A and #(J ) = #(L) = i .  ...  The ProtoBox package is the Maple implementation of some of our algorithms: the early terminations with thresholds in the Newton and Ben-Or/Tiwari algorithms, the racing algorithm that matches Newton against  ... 
doi:10.1016/s0747-7171(03)00088-9 fatcat:bna2bi7uzvh5nfvlbh2feg2kka

On sparse interpolation over finite fields

Seyed Mohammad Mahdi Javadi, Michael Monagan
2011 ACM SIGSAM Bulletin  
Ben-Or/Tiwari Sparse Interpolation Algorithm Let f be a polynomial with coefficients in Z. In Ben-Or/Tiwari sparse interpolation algorithm, the number of probes does not depend on the degree.  ...  Protobox In 2000 , 2000 Kaltofen et al., presented a hybrid of Zippel and Ben-Or Tiwari algorithms which they call a racing algorithm.  ... 
doi:10.1145/1940475.1940493 fatcat:p3isglx3ybbsdcahht77cumlty

Page 8568 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
are presented: Early termination with thresholds in dense interpolations in the standard basis; the Ben- Or-Tiwari sparse interpolation in the standard basis and early termination in this algorithm; univariate  ...  sparse interpolations in the Pochhammer basis and early termination in this algorithm; early termination of sparse interpolations in the Chebyshev basis and a modified Gohberg-Koltracht algorithm; racing  ... 

Fifteen years after DSC and WLSS2 what parallel computations I do today

Erich L. Kaltofen
2010 Proceedings of the 4th International Workshop on Parallel and Symbolic Computation - PASCO '10  
An important technique in symbolic computation is the evaluation/interpolation paradigm, and multivariate sparse polynomial parallel interpolation constitutes a keystone operation, for which we present  ...  a new algorithm.  ...  Acknowledgments: I thank Jean-Guillaume Dumas for sharing with me his experience with the memory bus contention problem and TCmalloc, and Marc Moreno Maza for his reviewing comments.  ... 
doi:10.1145/1837210.1837213 dblp:conf/cap/Kaltofen10 fatcat:sqdn5uoc2bbu7el2icq6f37tvi

Page 1297 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
Lobo, Early termination in Ben-Or/Tiwari sparse interpolation and a hy- brid of Zippel’s algorithm (192-201 (electronic)); Grégoire Lecerf, Computing an equidimensional decomposition of an algebraic va  ...  Raul Pérez, An exper- imental study about the search mechanism in the SLAVE learning algorithm: hill-climbing methods versus genetic algorithms (159- 174); Luciano Sanchez, Inés Couso and J.  ... 

On exact and approximate interpolation of sparse rational functions

Erich Kaltofen, Zhengfeng Yang
2007 Proceedings of the 2007 international symposium on Symbolic and algebraic computation - ISSAC '07  
Randomization and early termination strategies are exploited to minimize the number of black box evaluations.  ...  Finally, one can deploy the sparse rational function interpolation algorithm in the hybrid symbolic-numeric setting when the black box for the rational function returns real and complex values with noise  ...  Acknowledgement: We thank Wen-shin Lee for providing her numeric sparse interpolation code to us, Arne Storjohann for sending us [22] and discussions on rational vector recovery, and Lihong Zhi for discussions  ... 
doi:10.1145/1277548.1277577 dblp:conf/issac/KaltofenY07 fatcat:vumng65q5zdyvof4qg3z3gu3xu

Reconstructing Rational Functions with FireFly [article]

Jonas Klappert, Fabian Lange
2019 arXiv   pre-print
As an application, we use FireFly in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program Kira.  ...  We present the open-source C++ library FireFly for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation.  ...  The Feynman diagrams in this paper were drawn with Tik Z-Feynman [75] .  ... 
arXiv:1904.00009v1 fatcat:ksgwhettkrfodejxpp4epvf7ge

Page 2027 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel’s algorithm. — (with Corless, Robert M.; Jeffrey, David J.)  ...  (with Kryukov, A. P.; Rodionov, A. Ya.; Shpiz, G. B.) The use of group and algebraic properties of tensor expressions in an object-oriented computer algebra system. (Russian.  ... 

Page 1079 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Early termination in Ben- Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm. (see 2002b:68007) Katsoprinakis, E. (with Nestoridis, V.; Papadoperakis, I.) Universal Faber series.  ...  Interpolation formulas of Lagrange type in a Hilbert space that are invariant with respect to polynomials. (Russian.  ... 

Page 901 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel’s algorithm. Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St.  ...  Algebraic algorithms. Algorithms and theory of comy ion handbook, \6-\-16-27, CRC, Boca Raton, FL, 1999. (see 2001f:68001) 68W30 (13P99, 15-04, 65F30) — (with Lee, Wen-shin; Lobo, Austin A.)  ... 

Page 1187 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
Nikshych) 2002d:16045 16W30 (16D10) Lobo, Austin A. (with Kaltofen, Erich; Lee, Wen-shin) Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel’s algorithm.  ...  (English summary) Solving constraint problems with hybrid algorithms. Ann. Math. Artif.  ... 

Dagstuhl Reports, Volume 5, Issue 6, June 2015, Complete Issue [article]

2016
Prony's method appeared much later in the case of sparse polynomial interpolation with it's use by Blahout, Ben-or/Tiwari, and Giesbrecht/Labahn/Lee.  ...  In the case of sparse interpolation one encounters Zippel's method while in exponential analysis there are projection methods.  ...  I will present the background to and some features of model theoretic independence, giving a short overview of the roles of dependence and independence in classification theory.  ... 
doi:10.4230/dagrep.5.6 fatcat:p6ax7r2gsrfpnajg7dqggs5ffm

2015 Jahresbericht Annual Report

Registernummer Amtsgericht, Saarbrücken Hrb, Vorsitzender Des Aufsichtsrates, Ing, Jähnichen Stefan, Raimund Geschäftsführung, Seidel, Meißner Heike, Gesellschafter
unpublished
The organizers would like to express their gratitude to the participants and the Schloss Dagstuhl team for a productive and exciting seminar. We thank Prof.  ...  We would like to thank Dagmar Glaser and the staff at Schloss Dagstuhl for their continuous support and great hospitality which was the basis for the success of this seminar. Acknowledgements.  ...  Prony's method appeared much later in the case of sparse polynomial interpolation with it's use by Blahout, Ben-or/Tiwari, and Giesbrecht/Labahn/Lee.  ... 
fatcat:tzkatxrngzbj7j3qvr7j7znvla