Multipliers play a vital role in many cryptographic applications like elliptic curve cryptography, RSA and other algorithms. The direct truncation of least significant part of the product leads to large error in the resultant product when fixed width output is the requirement. This paper proposes a truncation error minimizing logic which greatly reduces truncation error. Truncation error minimi...

We introduce a variable timestepping algorithm for the Milstein scheme applied to SDEs with a scalar stochastic forcing. Multiple local error estimates are used, corresponding to different terms appearing in the Taylor series of the local truncation error. The timesteps are then chosen so as to bound the standard deviation of the contribution of each of these terms over a unit time interval, an...

Interpolation is a fundamental issue in image processing. In this short paper, we communicate ongoing results concerning the accuracy of two landmark approaches: the Shannon expansion and the Discrete Fourier Transform (DFT) interpolation. Among all sources of error, we focus on the impact of spatial truncation. Our estimations are expressed in the form of upper bounds on the Root Mean Squared ...

Cube propagation has been suggested as an alternative to Jacobian integration for estimating the volume change under a deformation in three dimensions [Pai et al., 2013]. Cube propagation estimates the change in volume by approximating a three dimensional volume as a mesh of tetrahedra, which covers the interior of the volume and approximates the boundary as piece-wise triangular surface patche...

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

A class of ^-stable advanced multistep methods is derived for the numerical solution of initial value problems in ordinary differential equations. The methods, of all orders of accuracy up to ten, only require values of y' and are self starting. Results for the asymptotic behaviour of the discretization error and for estimating local truncation error are also obtained. The practical implementat...

New expressions for one-sided finite-difference approximations are proposed. In these approximations the odd-order error terms are eliminated while the even-order terms are left to be taken care of by Richardson extrapolation. The effective local truncation error is shown to be less than for higher-order one-sided finite-difference approximations but the solutions for a test problem are shown t...

Optimal prediction is a computational method for systems that cannot be properly resolved, in which the unresolved variables are viewed as random. This paper presents a first analysis of optimal prediction as a numerical method. We prove the convergence of the scheme for a class of equations of Schrödinger type and derive error bounds for the mean error between the optimal prediction solution a...

As a byproduct of Theorem 3.1 we can give an estimate of the truncation error which arises if one ignores all the samples outside a finite interval. More precisely, we have the following corollary. Theorem 4.1: Let us define the truncation error E N (t) as follows: E N (t) = F(t) 0 jnjN F (t n)S n (t): Then jE N (t)j 2 2p0q bA p C ^ (1 0 p D)(p 0 q 0 1)N p0q01 ; t in the compact set K (14) wher...