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ARITH
2007
IEEE
13 years 9 months ago
Efficient polynomial L-approximations
We address the problem of computing a good floating-point-coefficient polynomial approximation to a function, with respect to the supremum norm. This is a key step in most process...
Nicolas Brisebarre, Sylvain Chevillard
SODA
1992
ACM
90views Algorithms» more  SODA 1992»
13 years 6 months ago
Self-Testing Polynomial Functions Efficiently and Over Rational Domains
In this paper we give the first self-testers and checkers for polynomials over rational and integer domains. We also show significantly stronger bounds on the efficiency of a simp...
Ronitt Rubinfeld, Madhu Sudan
CORR
2008
Springer
84views Education» more  CORR 2008»
13 years 5 months ago
Efficiently Testing Sparse GF(2) Polynomials
We give the first algorithm that is both query-efficient and time-efficient for testing whether an unknown function f : {0, 1}n {-1, 1} is an s-sparse GF(2) polynomial versus -far ...
Ilias Diakonikolas, Homin K. Lee, Kevin Matulef, R...
CORR
2008
Springer
125views Education» more  CORR 2008»
13 years 5 months ago
Simultaneous Modular Reduction and Kronecker Substitution for Small Finite Fields
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform sever...
Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy
ICMS
2010
13 years 3 months ago
Efficient Evaluation of Large Polynomials
Abstract. Minimizing the evaluation cost of a polynomial expression is a fundamental problem in computer science. We propose tools that, for a polynomial P given as the sum of its ...
Charles E. Leiserson, Liyun Li, Marc Moreno Maza, ...