A framework for generating a new class of numerical integration methods.

摘要

The calculation of integrals is a central task in many scientific and technological endeavors. Several attempts have been made to develop algorithms that minimize the errors in numerical integration problems. One such algorithm is the Romberg method. This method is a two-phase technique used to approximate an integral using Composite Trapezoid Rule (CTR) and Richardson extrapolation. It has been found that Richardson extrapolation can he represented by a fixed vector. This vector can then be used with the CTR result in order to approximate an integral. Through the research presented in this thesis, a genetic algorithm technique is developed to find an alternative vector that yields a better accuracy than Romberg method. This technique allows the use of methods other than CTR. By creating a method that is not bound to any specific numerical integration method, a new class of numerical integration methods is presented.