On computing sparse shifts for univariate polynomials
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Algorithms for computing sparse shifts for multivariate polynomials
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
On computing greatest common divisors with polynomials given by black boxes for their evaluations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
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
Sparse polynomial approximation in finite fields
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computer algebra handbook
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
A local decision test for sparse polynomials
Information Processing Letters
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Reconstructing sparse trigonometric functions
ACM Communications in Computer Algebra
Representation of sparse Legendre expansions
Journal of Symbolic Computation
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In this paper, we consider the problem of interpolating univariate polynomials over a field of characteristic zero that are sparse in (a) the Pochhammer basis or, (b) the Chebyshev basis. The polynomials are assumed to be given by black boxes, i.e., one can obtain the value of a polynomial at any point by querying its black box. We describe efficient new algorithms for these problems. Our algorithms may be regarded as generalizations of Ben-Or and Tiwari's (1988) algorithm (based on the BCH decoding algorithm) for interpolating polynomials that are sparse in the standard basis. The arithmetic complexity of the algorithms is $O(t^2 + t\log d)$ which is also the complexity of the univariate version of the Ben-Or and Tiwari algorithm. That algorithm and those presented here also share the requirement of $2t$ evaluation points.