Analysis of the total random error in simulation systems

Abstract

The article presents an analytical assessment of error in computer simulation systems for cases of an unknown arbitrary type of symmetric distributions of the total random error of calculations. The study is based on the use of asymptotic properties of a sequence of random variables. The work includes the development of a mathematical framework for predicting a confidence estimate of random error. An innovative approach to selecting the initial approximation is proposed. The proposed approach increases the efficiency of the iterative error calculation process. It has been established that, for any type of symmetric distribution laws, the series contains only integer powers of n. Using the established pattern ensures better convergence and optimizes the calculation of the numerical value of the modeling error. Simplified formulas have been created for calculating confidence intervals at high probability levels. The applicability conditions of the methodology have been determined. It has been experimentally confirmed that for a uniform distribution, acceptable accuracy is achieved with at least two components. At the same time, for a sinusoidal distribution, at least three components are needed to achieve an error below the acceptable limit. For high levels of modeling reliability, the required accuracy is achieved with two components without the need to introduce additional adjustments. The reliability of the obtained results was verified for two cases of input data. In the first case, the results of studies on modelling accuracy using the representation of numbers in the binary-hexadecimal system as arrays were used. In the second case, input data from error calculations of solving linear GPU NVIDIA tasks with floating-point representation were used. The methodology is universal and can be applied to both random and systematic errors that occur in simulation systems.