This paper determines the exact value of the n-term approximation of a diagonal linear operator from l M p to l M q , 0 < p, q ≤ ∞ using an elementary method. c © 2009 Elsevier Inc. All rights reserved.

We study the non-equilibrium dynamics of the O(N) model in classical and quantum field theory in 1+1 dimensions, forN > 1. We compare numerical results obtained using the Hartree approximation and two next to leading order approximations, the bare vertex approximation and the 2PI-1/N expansion. The later approximations differ through terms of order g, where g is the scaled coupling constant, g ...

The spectral vanishing viscosity (SVV) method was introduced in the late 80’s [24] in order to solve, with the spectral Fourier method, 1D non-linear conservations laws (typically, the inviscid Burgers equation). The non-periodic case was investigated later [16], using a Legendre polynomial approximation. In both cases the basic idea is to introduce a SVV term VN , only active in the high frequ...