This paper provides an a priori error analysis of localized orthogonal decomposition method for the numerical stochastic homogenization model random diffusion problem. If uniformly elliptic and bounded coefficient field problem is stationary satisfies quantitative decorrelation assumption in form spectral gap inequality, then expected $L^2$ can be estimated, up to logarithmic factors, by $H+(\v...

Modified Normalized Least Mean Square (MNLMS) algorithm, which is a sign form of NLMS based on set-membership (SM) theory in the class of optimal bounding ellipsoid (OBE) algorithms, requires a priori knowledge of error bounds that is unknown in most applications. In a special but popular case of measurement noise, a simple algorithm has been proposed. With some simulation examples the performa...

We give an error estimate for the Energy and Helicity Preserving Scheme (EHPS) in second order finite difference setting on axisymmetric incompressible flows with swirling velocity. This is accomplished by a weighted energy estimate, along with careful and nonstandard local truncation error analysis near the geometric singularity and a far field decay estimate for the stream function. A key ing...

1. Introduction. The problem of finding rational approximations to functions has received a considerable amount of attention recently, and many methods exist for finding such approximations. A brief survey of the most widely used methods has been given by Cheney and Southard [1]. In all problems of approximation, it is essential to know the truncation error which arises when the function is rep...

This paper considers a finite element approach to modeling electromagnetic waves in a periodic diffraction grating. In particular, an a priori error estimate associated with the α-quasi-periodic transformation is derived. This involves the solution of the associated Helmholtz problem being written as a product of e(iαx) and an unknown function called the α-quasi-periodic solution. To begin with...