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The polynomial time algorithm of Lenstra, Lenstra, and Lovász [15] for factoring integer polynomials and variants thereof have been widely used to show that various computational problems in number theory have polynomial time solutions. Among them is the p ...
Computations of irregular primes and associated cyclotomic invariants were extended to all primes up to twelve million using multisectioning/convolution methods and a novel approach which originated in the study of Stickelberger codes (Shokrollahi (1996)). ...
The medical image registration problem can be formulated as a nonlinear programming problem. To identify appropriate algorithms to solve it, it is critical to analyze the properties of the problem. In this paper, we consider the image registration problem ...
A transmitter and receiver need to be designed to guarantee reliable communication on any channel belonging to a given family of finite-state channels defined over common finite input, output, and state alphabets. Both the transmitter and receiver are assu ...
We investigate the question when a cyclic code is maximum distance separable (MDS). For codes of (co-)dimension 3, this question is related to permutation properties of the polynomial (xb - 1)/(x - 1) for a certain b. Using results on these polynomials we ...
Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain Ω=(−1,1)d (d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...
The aim of this paper is to overcome the well-known lack of p-optimality in hp-version discontinuous Galerkin (DG) discretizations for the numerical approximation of linear elliptic problems. For this purpose, we shall present and analyze a class of hp-DG ...
Derivative-free optimization involves the methods used to minimize an expensive objective functionwhen its derivatives are not available. We present here a trust-region algorithmbased on Radial Basis Functions (RBFs). The main originality of our approach i ...
We present an algorithm to factor multivariate polynomials over algebraic number fields that is polynomial-time in the degrees of the polynomial to be factored. The algorithm is an immediate generalization of the polynomial-time algorithm to factor univari ...
A new polynomial-time algorithm for the factorization of polynomials in two variables with rational coefficients is presented. The algorithm works by replacing one of the variables by an approximation of a transcendental number. It generalizes recent resul ...
