The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
A deterministic algorithm for sparse multivariate polynomial interpolation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Computational Complexity of Sparse Rational Interpolation
SIAM Journal on Computing
Asymptotically fast solution of Toeplitz-like singular linear systems
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Mathematics of Computation
FOXBOX: a system for manipulating symbolic objects in black box representation
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Modern Computer Algebra
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
P-adic reconstruction of rational numbers
ACM SIGSAM Bulletin
Symbolic-numeric sparse interpolation of multivariate polynomials
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Symbolic-Numeric Computation (Trends in Mathematics)
Symbolic-Numeric Computation (Trends in Mathematics)
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Numerical optimization in hybrid symbolic-numeric computation
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Optimization and NP_R-completeness of certain fewnomials
Proceedings of the 2009 conference on Symbolic numeric computation
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Blind image deconvolution via fast approximate GCD
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Sparse interpolation of multivariate rational functions
Theoretical Computer Science
Optimizing n-variate (n+k)-nomials for small k
Theoretical Computer Science
Vector rational number reconstruction
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Diversification improves interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Supersparse black box rational function interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Theoretical Computer Science
Sparse multivariate function recovery from values with noise and outlier errors
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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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 a sparse rational function. domization and early termination strategies are exploited to minimize the number of black box evaluations. In addition, rational number coefficients are recovered from modular images by rational vector recovery. The need for separate numerator and denominator size bounds is avoided via correction, and the modulus is minimized by use of lattice basis reduction, a process that can be applied to sparse rational function vector recovery itself. Finally, one can deploy sparse rational function interpolation algorithm in the hybrid symbolic-numeric setting when the black box for the function returns real and complex values with noise. We present and analyze five new algorithms for the above problems and demonstrate their effectiveness on a mark implementation.