A combination of curve fitting algorithms to collect a few training samples for function approximation

Abstract

The aim of this paper is to approximate the numerical result of executing a program/function with a number of input parameters and a single output value with a small number of training points. Curve fitting methods are preferred to nondeterministic methods such as neural network and fuzzing system methods, because they can provide relatively more accurate results with the less amount of member in the training dataset. However, curve fitting methods themselves are most often function specific and do not provide a general solution to the problem. These methods are most often targeted at fitting specific functions to their training dataset. To provide a general curve fitting method, in this paper, the use of a combination of Lagrange, Spline, and trigonometric interpolation methods are suggested. The Lagrange method fits polynomial functions of degree N to its training values. In order to improve the resultant fitted polynomial our combinatorial method combines Lagrange with the polynomial resulted from the Spline method. If the absolute error of the actual value and the predicted value of a function are not desired, the trigonometric interpolation methods that fit trigonometric functions can be applied. Our experiments with a number of benchmark examples demonstrate the relatively high accuracy of our combinational fitting method.