Digital computers have dramatically aided the application of mathematical models to problems of all kinds. For the most part computers have served as calculating engines, data retrieval and sorting devices, and lately as a powerful medium for visualization. Rarely have computers been used to...

Virtually all managerial decision involve qualitative and quantitative aspects. Both are important and need to be reflected in the final decision. Any knowledge support system which helps managers to take better decisions should be able to ensure that the qualitative aspects are fully reflected...

This paper deals with parameter estimation in the bounded-error context. A new approach, based on interval analysis, is proposed to compute guaranteed estimates of suitable characteristics of the set of all values of the parameter vector such that the error between the experimental data and the...

Floating-point arithmetic is the fast way to perform scientific and engineering calculations. Today, individual floating-point operations are maximally accurate as a rule. However, after only two or just a few operations, the result can be completely wrong. Computers now carry out up to 1011...

After having reviewed the CESTAC (Contrôle et Estimation STochastique des Arrondis de Calculs) method, which uses a probabilistic approach to round-off error analysis, a new arithmetic called stochastic arithmetic is presented in this paper. This new arithmetic covers a large part of the...

A computer-assisted method for improving the mean squared error (MSE) in estimation for parametric models is presented. Assuming existence of nontrivial sufficient statistics, the method involves generation of Monte Carlo samples from the conditional distribution of the observables, given the...

The paper deals with the development and implementation of symbolic algorithms for the support-operators method for construction of finite-difference schemes. i.e., discretization of partial differential equations (PDEs), on a nonorthogonal logically rectangular grid. The general description of...

Some embedded Runge-Kutta methods with minimal phase-lag for second-order periodic initial-value problems are developed. It should be noted that these embedded methods are based on the Runge-Kutta methods of algebraic order three, and on a new error estimation introduced in this paper. The...