Publications related to Degree of a polynomial

Computational Performance of a Parallelized Three-Dimensional High-Order Spectral Element Toolbox

Michel Deville, Nicolas Fietier, Vincent Keller, Roland Bouffanais, Jonas Marcel Lätt, Christoph Bosshard, Sohrab Jairo Kehtari, Christian Clémençon

In this paper, a comprehensive performance review of all MPI-based high-order three-dimensional spectral element method C++ toolbox is presented. The focus is put on the performance evaluation of aspects with a particular emphasis on the parallel efficienc ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2009

Finite-element preconditioning of G-NI spectral methods

Alfio Quarteroni

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain

\Omega = (-1, 1)^d

(d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...

2009

hp-Optimal discontinuous Galerkin methods for linear elliptic problems

Benjamin Stamm

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 ...

2007

Computing Gröbner fans

This paper presents algorithms for computing the Gröbner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Gröbner bases of the ideal. Our algorithms are based on a uniform definition of the Gröbner fan that applies ...

2007

Identification of a Two-Input System: Variance Analysis

Dominique Bonvin, Alireza Karimi, Ljubisa Miskovic

This paper examines the identification of a single-output two-input system. Motivated by an experiment design problem(should one excite the two inputs simultaneously or separately), we examine the effect of the (second) input signal on the variance of the ...

2005

Optimal regular LDPC codes for the binary erasure channel

Mohammad Amin Shokrollahi

We prove that for any given R between 0 and 1 the best threshold value for a regular LDPC code of rate R with common variable degree v and common check degree c occurs when v is at least 3 and is minimal subject to the condition

R=1-v/c

...

2005

Deciding properties of number fields without factoring

Mohammad Amin Shokrollahi

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 ...

1997

Degree of a polynomial

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Computational Performance of a Parallelized Three-Dimensional High-Order Spectral Element Toolbox

Finite-element preconditioning of G-NI spectral methods

hp-Optimal discontinuous Galerkin methods for linear elliptic problems

Computing Gröbner fans

Identification of a Two-Input System: Variance Analysis

Optimal regular LDPC codes for the binary erasure channel

Deciding properties of number fields without factoring

Identification of a Two-Input System: Variance Analysis

Optimal regular LDPC codes for the binary erasure channel

Deciding properties of number fields without factoring

Computational Performance of a Parallelized Three-Dimensional High-Order Spectral Element Toolbox

hp-Optimal discontinuous Galerkin methods for linear elliptic problems

Finite-element preconditioning of G-NI spectral methods

Computing Gröbner fans