Towards the best points of interpolation using particles swarm optimisation approach

Many studies, mostly empirical, have been devoted to finding optimal choice nodes for interpolating. When exploring the underlying factors that determine what is a good such choice, we are led to consider the Runge phenomenon (RP; best known in case of high order polynomial interpolation) as a key error mechanism. However, we shall see by using PSO that interpolation with polynomials of high degree can be very useful for the obtaining of the estimates of functions. This paper presents the advantage of using the Particle Swarm Optimization (PSO) interpolation nodes. PSO is a technique based on the cooperation between particles. The exchange of information between these particles allows to resolve difficult problems.