A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2010; you can also visit the original URL.
The file type is application/pdf.
Filters
Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields
1990
SIAM journal on computing (Print)
Preserved Fulltext
Key words, sparse multivariate polynomials, finite fields, interpolation AMS(MOS) subject classifications. 68C25, 12C05 GF[qr21g"n'+3], and (2) using inductive enumeration of partial solutions for terms ...
This algorithm yields the first efficient deterministic polynomial time algorithm (and moreover boolean NC-algorithm) for interpolating t-sparse polynomials over finite fields and should be contrasted ...
We are grateful to Michael Ben-Or, Johannes Grabmeier, Michael Rabin, Volker Strassen, and Avi Wigderson for a number of interesting conversations. ...
doi:10.1137/0219073
fatcat:ms2ohrjgqjddjprlwezcjesqn4
Diversification improves interpolation
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We consider the problem of interpolating an unknown multivariate polynomial with coefficients taken from a finite field or as numerical approximations of complex numbers. ...
Building on the recent work of Garg and Schost, we improve on the best-known algorithm for interpolation over large finite fields by presenting a Las Vegas randomized algorithm that uses fewer black box ...
The comments and suggestions of the anonymous referees were also very helpful, in particular regarding connections to previous results and the proof of Theorem 3.1. ...
arXiv:1101.3682v3
fatcat:zavsjkp4cjaafd77hgav7dmwce
Page 834 of Mathematical Reviews Vol. , Issue 97B
[page]
1997
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Summary: “We develop a randomized parallel algorithm which performs interpolation of sparse multivariate polynomials over finite fields. ...
As applications, we obtain efficient parallel algorithms for sparse multivariate polynomial factorization and GCD over finite fields. ...
Diversification improves interpolation
2011
Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Background
Finite Fields
Approximate Complex
Multivariate and beyond
Sparse interpolation algorithms over finite fields
• Dense methods (Newton/Waring/Lagrange): O˜(d) total cost. ...
We first consider univariate interpolation over finite fields. ...
doi:10.1145/1993886.1993909
dblp:conf/issac/GiesbrechtR11
fatcat:7rmfxz4iwfaeto7vwpfxhc4bcq
Special issue computational algebraic complexity editorial
1990
Journal of symbolic computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The article by Zippel deals with the problem of interpolating a sparse multivariate polynomial over fields of characteristic zero from its values. ...
result in a collection of surprisingly effective algorithms for sparse multivariate polynomial interpolation, which are presented here. ...
doi:10.1016/s0747-7171(08)80010-7
fatcat:wrri7sabmjb4tpqtqyfbwuoa6e
Page 815 of Mathematical Reviews Vol. , Issue 2001B
[page]
2001
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
of sparse multivariate polynomials over large finite fields with applications. ...
The authors develop a Las Vegas randomized algorithm for sparse polynomial interpolation over finite fields. ...
Sparse Polynomial Interpolation Based on Diversification
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We consider the problem of interpolating a sparse multivariate polynomial over a finite field, represented with a black box. ...
Building on the algorithm of Ben-Or and Tiwari for interpolating polynomials over rings with characteristic zero, we develop a new Monte Carlo algorithm over the finite field by doing additional probes ...
In 2001, Klivans and Spielman gave the first deterministic polynomial time algorithms for sparse interpolation over finite fields with large characteristic. ...
arXiv:2002.03706v1
fatcat:2dngbk4z3bdktihacrjma3tm4e
Reconstructing Rational Functions with FireFly
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
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. ...
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. ...
The Feynman diagrams in this paper were drawn with Tik Z-Feynman [75] . ...
arXiv:1904.00009v1
fatcat:ksgwhettkrfodejxpp4epvf7ge
Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Numerical results are presented underscoring the validity of sparse polynomial approximations and comparing with established reduced basis techniques. ...
The findings establish sparse polynomial interpolation as another instrument in the toolbox of methods for breaking the curse of dimensionality. ...
Acknowledgements We acknowledge the support provided by the European Research Council Executive Agency by the Consolidator Grant project AROMA-CFD "Advanced Reduced Order Methods with Applications in Computational ...
arXiv:2201.03228v1
fatcat:u2brlztnnfafhdezbthht5vkxa
Efficient techniques for multipolynomial resultant algorithms
1991
Proceedings of the 1991 international symposium on Symbolic and algebraic computation - ISSAC '91
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2006; you can also visit the original URL.
The file type is application/pdf.
upon the application).
3.1
Multivariate
Interpolation
oft he resulting matrix is a polynomial. ...
The timings correspond to a single iteration over a finite field and typically 3 -4 iterations are required. ...
doi:10.1145/120694.120706
dblp:conf/issac/ManochaC91
fatcat:moothyqmyrbmbpuuyqow5azm5y
Theoretical Properties
[chapter]
2013
Handbook of Finite Fields
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is application/pdf.
large finite field are NP-or co-NP-hard. ...
Here we have a situation where factoring over the rational numbers is provably easier than factoring over a sufficiently large finite field. ...
Minkowski sum, 9 Newton polytope, 9 NP-hardness, 11 Ostrowski theorem, 9 separable factorization, 3 sparse factorization, 9 sparse polynomial representation, 9 straight-line program, 11, 12 straight-line ...
doi:10.1201/b15006-5
fatcat:cubpnr7y3fbfpivjinvw2dqmvy
Theoretical Properties
[chapter]
2011
Chapman & Hall/CRC Biostatistics Series
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is application/pdf.
large finite field are NP-or co-NP-hard. ...
Here we have a situation where factoring over the rational numbers is provably easier than factoring over a sufficiently large finite field. ...
Minkowski sum, 9 Newton polytope, 9 NP-hardness, 11 Ostrowski theorem, 9 separable factorization, 3 sparse factorization, 9 sparse polynomial representation, 9 straight-line program, 11, 12 straight-line ...
doi:10.1201/b10783-7
fatcat:zqyyjtuzsjf7zpekrozupsqwye
Theoretical Properties
[chapter]
2015
The Fence Methods
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is application/pdf.
large finite field are NP-or co-NP-hard. ...
Here we have a situation where factoring over the rational numbers is provably easier than factoring over a sufficiently large finite field. ...
Minkowski sum, 9 Newton polytope, 9 NP-hardness, 11 Ostrowski theorem, 9 separable factorization, 3 sparse factorization, 9 sparse polynomial representation, 9 straight-line program, 11, 12 straight-line ...
doi:10.1142/9789814596077_0009
fatcat:7rmqxc74afagha2moms4jjz35u
A deterministic multivariate interpolation algorithm for small finite fields
2002
IEEE transactions on computers
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We present a new multivariate interpolation algorithm over arbitrary fields which is primarily suited for small finite fields. ...
Given function values at arbitrary t points, we show that it is possible to find an n-variable interpolating polynomial with at most t terms, using the number of field operations that is polynomial in ...
Anonymous reviewers provided invaluable help in improving the final presentation of the paper. ...
doi:10.1109/tc.2002.1032628
fatcat:3kzrygdxrffc5fuf2rfg54aoky
Sparse interpolation of multivariate rational functions
2011
Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Our method can be combined with probabilistic and deterministic components from sparse polynomial black box interpolation to suit either an exact or a finite precision computational environment. ...
The latter is illustrated with several examples, running from exact finite field arithmetic to noisy floating point evaluations. ...
Acknowledgements We thank Erich Kaltofen and Zhengfeng Yang for valuable remarks and providing their sparse rational interpolation codes and benchmarks. ...
doi:10.1016/j.tcs.2010.11.050
fatcat:pmnhbkkj3zethawvfmovzdnohq
« Previous
Showing results 1 — 15 out of 3,207 results