Computer Technology for Construction ε-Solution of the Problem

Abstract

Introduction. Issues of selection and construction of computing resources and methods of their effective use to calculate an approximate solution of the problem with the given accuracy in a limited processor time are considered. The purpose of the article. Based on the analysis of the total error of the computational algorithm, to develop a computer technology (CT) for the construction and solution of the ε-problem and illustrate it on the problems of integrating rapidly oscillating functions and digital signal processing. The results. The general scheme for solving problems of applied and computational mathematics using computer technology is presented. Computer technology includes the formation of a certain set of computing resources, the method and conditions of their use to build a computing process, the result of which should be the solution of the problem. The main attention is paid to the choice of a computer calculations model (input data about the problem, the class of problems of computational mathematics, the class of computational algorithms for calculating the solution, evaluation of quality characteristics and parameters of the computational process, computer architecture, software, restrictions on the value of quality characteristics), the construction of quality characteristic estimates, the possibility of adjusting the mathematical model, the construction of the computational process and the performance of calculations. The issues of determining the optimal parameters of computational algorithms-programs for finding ε-solution are investigated, which are demonstrated on two classes of problems – integration of rapidly oscillating functions and correlation analysis of random processes. Conclusions. The issues of selection and construction of computing resources and methods of their effective use to calculate an approximate solution of the problem with the given accuracy in a limited processor time are considered. The elements of computer technology for solving specific problems on the examples of problems of integration of rapidly oscillating functions and correlation analysis of random processes are applied. Keywords: total error, computer technology, rounding error, rapidly oscillating functions.