One of the most important problem for solving the linear system Ax = b, by using the iterative methods, is to use a good stopping criterion and to determine the common significant digits between each corresponding components of computed solution and exact solution. In this paper, for a certain class of iterative methods, we propose a way to determine the number of common significant digits of x...

The aim of this work, is to evaluate the value of a fuzzy integral by applying the Newton-Cotes integration rules via a reliable scheme. In order to perform the numerical examples, the CADNA (Control of Accuracy and Debugging for Numerical Applications) library and the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method are applied based on the stochastic arithmetic. By ...

Over the past several years a number of hybrid algorithms have been proposed for solving large sparse systems of linear algebraic equations. In this paper we consider the hybrid GMRES algorithm by Nachtigal, Reichel and Trefethen (1992) and show that in the floating-point arithmetic there exist some cases in which the properties of this algorithm are lost, e.g., the result is false, or the coef...

The aim of this paper is to present a new method and the tool validate numerical results Volterra integral equation with discontinuous kernels in linear non-linear forms obtained from Adomian decomposition method. Because disadvantages traditional absolute error show accuracy mathematical methods which based on floating point arithmetic, we apply stochastic arithmetic condition study efficiency...

The researchers aimed to study the nonlinear fractional order model of malaria infection based on Caputo-Fabrizio derivative. homotopy analysis transform method (HATM) is applied floating-point arithmetic (FPA) and discrete stochastic (DSA). In FPA, show accuracy we use absolute error which depends exact solution a positive value ?. Because in real life problems do not have optimal ?, need intr...

Numerical verification of industrial codes, such as those developed at Électricit e de France (EDF) R&D, requires estimating the precision and the quality of computed results, which is even more challenging for codes running in HPC environments where billions of instructions are performed each second, usually using external libraries (e.g., MPI, BLACS, BLAS, LAPACK). In this context, one needs ...

The CESTACmethod and its implementation known as CADNA software have been created to estimate the accuracy of the solution of real life problems when these solutions are obtained from numerical methods implemented on a computer. The method takes into account uncertainties on data and round-off errors. On another hand a theoretical model for this method in which operands are gaussian variables c...