We consider a class of interpolation algorithms, including the least-squares optimal Yen interpolator, and we derive a closed-form expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix that is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The...

‎‎In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...

This paper presents the application of Sinc method to solve second order two-point boundary value problems based on derivative interpolation. Even in the presence of singularities, the Sinc numerical method is known to exhibit exponential convergence, resulting in highly accurate solutions. However, the customary approach of interpolating the solution variable with the Sinc bases requires first...

BACKGROUND Electrical Impedance Tomography (EIT) is used as a fast clinical imaging technique for monitoring the health of the human organs such as lungs, heart, brain and breast. Each practical EIT reconstruction algorithm should be efficient enough in terms of convergence rate, and accuracy. The main objective of this study is to investigate the feasibility of precise empirical conductivity i...

Abstract An efficient direct domain decomposition method is developed coupled with Poly-Sinc approximation over complex geometry. We solve 2D Poisson equations in L-Shaped geometry. The spatial domains of interest are decomposed into several non-overlapping rectangular subdomains. In each sub-domain, a Poly-Sinc collocation scheme is used to approximate the solution of the governing equation. S...

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

Contents Abstract Sinc approximation methods excel for problems whose solutions may have singularities, or innnite domains, or boundary layers. This article summarizes results obtained to date, on Sinc numerical methods of computation. Sinc methods provide procedures for function approximation over bounded or unbounded regions, encompassing interpolation, approximation of derivatives, approxima...

A number of problems in image reconstruction and image processing can be addressed, in principle, using the sinc kernel. Since the sinc kernel decays slowly, however, it is generally avoided in favor of some more local but less precise choice. In this paper, we describe the fast sinc transform, an algorithm which computes the convolution of arbitrarily spaced data with the sinc kernel in O.N lo...