Suspension bridge effect — A consideration about numerical precision of the natural neighbor interpolation

Abstract

The natural neighbor interpolation is an interpolation method based on Voronoi diagrams. Since it treats the given data naturally, it has a lot of merits that the finite element method does not have. This fact seems to suggest that the precision of the natural neighbor interpolation is better than that of the finite element method when they are used for function approximation. This paper examines whether this conjecture is true by a numerical experiment. From the experiment, it is observed that the precision of the natural neighbor interpolation is slightly worse than that of the finite element method. This paper discusses the reason why, and concludes that it is caused by an unwanted property of natural neighbor interpolants, which is called the suspension bridge effect in this paper.