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We consider the problem of sparse interpolation of an approximate multivariate black-box polynomial in floating-point arithmetic. ... By interpolating the black box evaluated at random primitive roots of unity, we give efficient and numerically robust solutions. ... Numerical methods for sparse interpolation In this section we present two methods for black-box interpolation of sparse multivariate polynomials in floating-point arithmetic. ...doi:10.1016/j.jsc.2008.11.003 fatcat:hfy7ywxe2rbszp6wkqv7ruukoi
We consider the problem of sparse interpolation of an approximate multivariate black-box polynomial in floating-point arithmetic. ... By interpolating the black box evaluated at random primitive roots of unity, we give efficient and numerically robust solutions. ... Numerical methods for sparse interpolation In this section we present two methods for black-box interpolation of sparse multivariate polynomials in floating-point arithmetic. ...doi:10.1145/1145768.1145792 dblp:conf/issac/GiesbrechtLL06 fatcat:sjord5m22zddxmkzvjbcyc322a
Texts & Monographs in Symbolic Computation
Exact polynomial and differential algebra, Gröbner bases SymDwf 3. Inverse symbolic problems, e.g., interpolation and parameterization SymDwf 4. Tarski's algebraic theory of real geometry SymDwf 5. ... Hybrid symbolic-numeric computation SymDwf 6. Computation of closed form solutions SymDwf 7. ... Zippel's  and Ben-Or and Tiwari's  sparse multivariate polynomial algorithms are a fundamental contribution from symbolic computation to the task of function/model recovery. ...doi:10.1007/978-3-7091-0794-2_5 fatcat:y6fjj6ghrzek5ps4vig7uv5vpy
., besides the latter areas, our special issue treats decomposition of a multivariate polynomial into the sum of squares, sparse multivariate polynomial interpolation, ill conditioned linear systems of ... set of univariate or multivariate polynomials. ... Cuyt and Lee present a deterministic numerical algorithm for sparse multivariate polynomial interpolation, which requires no information on the number of terms or the partial degree in each variable. ...doi:10.1016/j.tcs.2008.09.001 fatcat:uwwutxg5svdkholg7mtcu2pvzy
F.(1987) figuration space for curved objects for robot motion planning. 6 "A deter- ministic algorithm for sparse multivariate polynomial interpolation", 20th Annual ACM Symp. ... upon the application). 3.1 Multivariate Interpolation oft he resulting matrix is a polynomial. ...doi:10.1145/120694.120706 dblp:conf/issac/ManochaC91 fatcat:moothyqmyrbmbpuuyqow5azm5y
The problem of interpolating multivariate polynomials whose coefficient domain is the rational numbers is considered. ... The effect of intermediate number growth on a speeded Ben-Or and Tiwari algorithm is studied. Then the newly developed modular algorithm is presented. ... Here we report how these techniques can be applied to the problem of interpolating sparse multivariate polynomials. ...doi:10.1145/96877.96912 dblp:conf/issac/KaltofenLW90 fatcat:hhpu6eq7tjflbhhren66cvwyle
In general, the performance of our sparse rational black box interpolation depends on the choice of the employed sparse polynomial black box interpolation. ... Consider the black box interpolation of a τ -sparse, n-variate rational function f , where τ is the maximum number of terms in either numerator or denominator. ... 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
(English summary) Parallel symbolic computation. J. Symbolic Comput. 21 (1996), no. 4-6, 377-396. Summary: “A new algorithm for sparse multivariate polynomial interpolation is presented. ... multivariate polynomial interpolation and its parallel implementation. ...
Summary: “We consider the problem of interpolating sparse mul- tivariate polynomials from their values. ... Miihlbach (D-HANN-AM) 91a:65014 65D05 Kaltofen, Erich (1-RSP-C); Yagati, Lakshman (1-RSP-C) Improved sparse multivariate polynomial interpolation algorithms. ...
Our multivariate polynomial and rational function interpolation algorithm combines Zippel's symbolic sparse polynomial interpolation technique [Ph.D. ... Our multivariate algorithm can build a sparse model from a number of evaluations that is linear in the sparsity of the model. ... Note that in [2, Section 3] we have shown stability for a numerical version of Blahut's errorcorrecting polynomial interpolation algorithm for E = 1. 2. an exact interpolation algorithm for sparse multivariate ...doi:10.1145/2465506.2465524 dblp:conf/issac/KaltofenY13 fatcat:ccdgfxh7cjckvj5lneljnwblue
In this tutorial we examine the state of the art for sparse polynomial algorithms in three areas: arithmetic, interpolation, and factorization. ... Simply put, a sparse polynomial is one whose zero coefficients are not explicitly stored. ... An even more difficult problem is sparse rational function interpolation, which is the same as sparse polynomial interpolation except that the unknown f is a fraction of two sparse multivariate polynomials ...doi:10.1145/3208976.3209027 dblp:conf/issac/Roche18 fatcat:fygzzsxjwrdk7kfxw4z4g7zsjq
The algorithm can also be used for interpolating polynomials from their values and expanding symbolic determinants. ... Recently, the techniques of Gr} obner bases and polynomial continuationhave received much attention as algorithmic methods for these symbolic and numeric applications. ... This problem arises in symbolic and numeric techniques used to manipulate sets of polynomial equations. ...doi:10.1006/jsco.1993.1009 fatcat:esj7dbw5kfh5njozjiktvn5arq
The black box algorithm for separating the numerator from the denominator of a multivariate rational function can be combined with sparse multivariate polynomial interpolation algorithms to interpolate ... 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  and discussions on rational vector recovery, and Lihong Zhi for discussions ...doi:10.1145/1277548.1277577 dblp:conf/issac/KaltofenY07 fatcat:vumng65q5zdyvof4qg3z3gu3xu
Some numerical ingredients We show that the sparse interpolation problem is well-posed for evaluations at low-order roots of unity: Theorem Suppose f , g ∈ C[x] , p is a randomly-chosen "good prime", ∈ ... Cost of our algorithm: O(n 2 t 2 log 2 d).Zippel's method. Go variable-by-variable; at each of n steps perform univariate interpolation t times on degree-d polynomials. ...doi:10.1145/1993886.1993909 dblp:conf/issac/GiesbrechtR11 fatcat:7rmfxz4iwfaeto7vwpfxhc4bcq
result in a collection of surprisingly effective algorithms for sparse multivariate polynomial interpolation, which are presented here. ... The article by Zippel deals with the problem of interpolating a sparse multivariate polynomial over fields of characteristic zero from its values. ...doi:10.1016/s0747-7171(08)80010-7 fatcat:wrri7sabmjb4tpqtqyfbwuoa6e
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