<b>Random points generation in Rⁿ</b> - DOI: 10.4025/actascitechnol.v25i2.2215

Abstract

There is a large interest on random number generation for its importance in several areas as statistics, simulation, optimization by mean of heuristic process, etc. This paper in particular was developed based on a research where it was necessary to produce random points in a cube of Rⁿ. The initial idea to produce a random point was to generate n random real numbers x₁, x₂, ..., x_n uniformly distributed in the [-L/2, L/2] interval, where L is the measure of the edges, and to build the point X = (x₁, x₂, ..., x_n). However, it was noticed that most of the points produced on this manner were too near to the frontier of cube, what was not of interest to the research. This paper aims to show the reasons why this problem occurs and to present a single algorithm to solve it. Several sequences of 4000 points each in cubes of Rⁿ were generated utilizing this algorithm, for different values of n. The analysis of data showed that the algorithm had a good performance, generating well distributed points in these regions.