We demonstrate the power of a recently proposed approximation scheme for the nonperturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow equations obtained within this scheme and compute the two-point functions of the O(N) theories at criticality, in two and three dimensions. Excellent results are o...

In this paper we generalize the notion of polynomial-time approximation scheme preserving reducibility, called PTAS-reducibility, introduced in a previous paper. As a rst application of this generalization, we prove the APX-completeness of a polynomially bounded optimization problem, that is, an APX problem whose measure function is bounded by a polynomial in the length of the instance and such...

in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

the electronic structure, energy band structure and electronic density of 2 sno ceramic in cubicphase have been investigated using first principle full potential-linearized augmented plane wave (fp-lapw)method within density functional theory (dft). local density approximation (lda) and the generalizedgradient approximation (gga), which are based on exchange- correlation energy optimization wer...

We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between t...

The full discretization of the semilinear stochastic wave equation is considered. discontinuous Galerkin finite element method used in space and analyzed a semigroup framework, an explicit position Verlet scheme for temporal approximation. We study stability under CFL condition prove optimal strong convergence rates fully discrete scheme. Numerical experiments illustrate our theoretical results...

R. Speck∗†, D. Ruprecht†, M. Emmett‡, M. Minion§, M. Bolten¶ R. Krause†, ∗Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany. †Institute of Computational Science, Università della Svizzera italiana, Switzerland. ‡Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, USA. §Institute for Computational and Mathematical Engineering, Stanford Universi...

For the numerical solution of time-dependent partial differential equations, time-parallel methods have recently shown to provide a promising way to extend prevailing strong-scaling limits of numerical codes. One of the most complex methods in this field is the “Parallel Full Approximation Scheme in Space and Time” (PFASST). PFASST already shows promising results for many use cases and many mor...

This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates. Our scheme is very effective fo...