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7 papers · 1 filter
Sparse Polynomial Interpolation and Division in Soft-linear Time
Pascal Giorgi, Bruno Grenet, Armelle Perret du Cray +1
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms to recover its nonzero coefficients and corresponding exponents. As an applicatio…
Generic reductions for in-place polynomial multiplication
Pascal Giorgi, Bruno Grenet, Daniel Roche
The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best p…
LU factorization with errors *
Jean-Guillaume Dumas, Joris Van Der Hoeven, Clément Pernet +1
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main alg…
Parallel sparse interpolation using small primes
Mohamed Khochtali, Daniel S. Roche, Xisen Tian
To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based "big prime" technique, which acts over a single large finite field…
Output-sensitive algorithms for sumset and sparse polynomial multiplication
Andrew Arnold, Daniel S. Roche
We present randomized algorithms to compute the sumset (Minkowski sum) of two integer sets, and to multiply two univariate integer polynomials given by sparse representations. Our…
Faster Sparse Multivariate Polynomial Interpolation of Straight-Line Programs
Andrew Arnold, Mark Giesbrecht, Daniel S. Roche
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algo…