Searching globally optimal parameter sequence for defeating Runge phenomenon by immunity genetic algorithm

摘要

Data interpolation is a fundamental data processing tool in scientific studies and engineering applications. However, when interpolating data points on an equidistant grid using polynomials, the so-called Runge phenomenon may occur, making polynomial interpolation unreliable. Although there are some methods proposed to defeat the Runge phenomenon, it is still an open problem which parameter sequence is the globally optimal for overcoming the Runge phenomenon. In this paper, we develop an immunity genetic algorithm based method to solve this problem. Specifically, we first model the Runge-phenomenon-defeating problem as an optimization in which the objective function is the energy of the parametric curve. An immunity genetic algorithm is then devised to determine the best IGA parameter sequence, which minimizes the objective function. The resulting parametric curve overcomes the Runge phenomenon. By performing the proposed immunity genetic searching algorithm starting with some groups of randomly generated parameter sequences, the resulted parameter sequences closely oscillate around the Chebyshev parameter sequence. Therefore, the Chebyshev parameter sequence is most likely the globally optimal sequence conquering the Runge phenomenon.