The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation still works accurately when combined with a proper variable transformation. The convergence rate has been analyzed for typical cases including finite, semi-infinite, and infinite intervals....

The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation. Their convergence rates have been analyzed for typical cases including finite, semi-infinite, and infinite intervals. In addition, for verified automatic integra...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

A fast multilevel algorithm (MuST) for evaluating an n-sample sinc interpolant at mn points is presented. For uniform grids, its complexity is 25mn log(1/δ) flops for the sinc kernel and 75mn log(1/δ) for the sincd kernel, where δ is the target evaluation accuracy. MuST is faster than FFTand FMM-based evaluations for large n and/or for large δ. It is also applicable to non-uniform grids and to ...

Perceived blur is an important measure of image quality and clinical visual function. The magnitude of image blur varies across space and time under natural viewing conditions owing to changes in pupil size and accommodation. Blur is frequently studied in the laboratory with a variety of digital filters, without comparing how the choice of filter affects blur perception. We examine the percepti...

A series of problems in different fields such as physics and chemistry are modeled by differential equations. Differential equations are divided into partial differential equations and ordinary differential equations which can be linear or nonlinear. One approach to solve those kinds of equations is using orthogonal functions into spectral methods. In this paper, we firstly describe Laguerre, H...

The current version allows for five different PSF models: The Gaussian model simulates a blurring effect by setting three different variance values. These values characterize the width of the PSF at various axial positions along the z-stack. The defocus model is simulated in the Fourier domain by a modulated Gaussian where the sinc modulation depends on the axial defocusing distance. Another de...