We study -splines (existence, uniqueness and convergence) in Banach spaces with a view to applications in approximation. Our approach allows, in particular, considering some problems in a more regular domain, and hence facilitating their solution.
We present the formulation of optical diffraction problem on periodic interface based on vector tangential fields, for which the system of boundary integral equations is established. Obtained mathematical model is numerically solved using boundary element method and applied to sine interface profile.
Optical diffraction for periodical interface belongs to relatively fewer exploited application of boundary integral equations method. Our contribution presents the formulation of diffraction problem based on vector tangential fields, for which the periodical Green function of Helmholtz equation is of key importance. There are discussed properties of obtained boundary operators with singular kernel and a numerical implementation is proposed.
In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order...
In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell’s equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order...
We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even...
The testing problem on the first-order autoregressive parameter in finite sample case is considered. The innovations are distributed according to the exponential distribution. The aim of this paper is to study how much the size of this test changes when, at some time k, an innovation outlier contaminant occurs. We show that the test is rather sensitive to these changes.
Some dynamical systems are characterized by more than one time-scale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of...