Random v/s Equispaced Points for One Dimensional Monte Carlo Integration

Abstract

Monte Carlo Method has been using in various fields of science, technology, research and management since a very long time. So far only random numbers have been considered for this method and research have been extended only to increase the randomness of these numbers. Instead of evaluating the function over the random points in the given range of integration by Monte Carlo Method we first divide the range of integration into n equal interval, obtain n equispaced points and then evaluate the integral over these points. Now we are interested to know that how does the choice of numbers (Random or Equispaced) affect the accuracy of one dimensional integral. Hence in this research work we are going to evaluate the one dimensional integral by Monte Carlo Method using random and equispaced points and will prove that equispaced points play a great role as far as the accuracy of one dimensional integral and pattern of decrement of error is concerned.