Integration of Functions
The results clearly show that the trapeze algorithm is ruled out as a practical method by not converging quickly
towards a solution.
Romberg's algorithm is the clear winner. At a given precision, it requires the least number of iterations. This is the
algorithm of choice in most cases.
Simpson's algorithm may be useful if the required precision is not too high and if the time to evaluate the function is small
compared to the interpolation. In such cases, Simpson's algorithm can be faster than Romberg's algorithm.
The following are the results for the "Integration of Functions" integration approximation research.