Monotonicity of one or more derivatives of the integrand is shown to imply a corresponding property of the approximating Romberg scheme. This is of importance in connection with error estimation by majorants [6]. The monotonicity properties are derived from an elementary study of the kernel functions involved. A possible explanation is given of the monotonicity which frequently occurs in applic...

Many problems in modern nancial economics involve the solution of continuous-time, continuous-state stochastic control problems. Since explicit solutions of such problems are extremely rare, e cient numerical methods are called for. The Markov chain approximation approach provides a class of methods that are simple to understand and implement. In this paper, we compare the performance of di ere...

Asymptotic expansions for the RT (Raviart-Thomas) mixed finite element approximation by the lowest-order rectangular element associated with a second-order elliptic equation on a rectangular domain are derived. Superconvergence for the vector field along the Gauss lines is obtained as a result of the expansion. A procedure of postprocessed extrapolation is presented for the scalar field, as wel...

In this paper, an iterative method for robust deconvolution with positivity constraints is discussed. It is based on the known variational interpretation of the Richardson-Lucy iterative deconvolution as fixed-point iteration for the minimisation of an information divergence functional under a multiplicative perturbation model. The asymmetric penaliser function involved in this functional is th...

Richardson Extrapolation is a powerful computational tool which can successfully be used in the efforts to improve the accuracy of the approximate solutions of systems of ordinary differential equations (ODEs) obtained by different numerical methods (including here combined numerical methods consisting of appropriately chosen splitting procedures and classical numerical methods). Some stability...

In microscopy, shot noise dominates image formation, which can be modeled as a Poisson process. The Richardson-Lucy method tends to converge slowly for large problems and is not flexible to the addition of nondifferentiable priors. In this project, proximal algorithms like ADMM and Chambolle-Pock are applied to three dimensional deconvolution and are shown to converge faster than Richardson-Lucy.

Abstract   In the present study, the effects of wavy wall’s properties on mixed convection heat transfer of Water-Al2O3 Nanofluid in a lid-driven cavity are investigated using the Lattice Boltzmann Method. The Boundary Fitting Method with second order accuracy at both velocity and temperature fields is used to simulate the curved boundaries in the LBM. The problem is investigated for different ...