Scattered data interpolation: tests of some methods

Abstract

Abstract. This paper is concerned with the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods. The process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation. To indicate the flavor of the type of results obtained, we give a summary table and representative perspective plots of several surfaces.

Numerical solution of differential equations using multiquadric radial basis function networks

“…It has been proved that radial basis function networks (RBFNs) with one hidden layer are capable of universal approximation (Park and Sandberg, 1993). For problems of interpolation and approximation of scattered data, there is a body of evidence to indicate that the multiquadric function (MQ) yields more accurate results in comparison with other radial basis functions (Franke, 1982Powell, 1988Haykin, 1999. Although it is not proved even experimentally in the present w ork that MQ function would result in superior accuracy for solving DEs, the MQ function is used to study the solution of DEs in this paper based on the above observation because the main aim of the present w ork is to demonstrate the procedure for solving DEs rather than the study of the property o f t h e k ernels.…”

Interpolating sparse scattered data using flow information

“…The problem of scattered data interpolation has a long history, and a large variety of methods have been proposed for its solution [2]. One of the earliest approaches, proposed by Shepard [3], used inverse distance weighting to weight the scattered samples.…”

“…For large data sets, global methods can be computationally prohibitive in practice. For this reason, local versions of these methods have been developed [2]. These restrict the number of data points that are used to compute each point of the reconstructed field.…”

“…The flow-based non-Euclidean distance between points x i and x j is dsym(x i , x j ), which is computed according to Eqs. (1) and (2). The across-streamline distances d1(x i , x j ) and d1(x j , x i ) are the lengths of the magenta line segments in the diagram, while the along-streamline distances d2(x i , x j ) and d2(x j , x i ) are the lengths of the green curves.…”

“…Many different methods have been proposed for the reconstruction of scalar fields based on scattered observations [2][3][4][5][6][7][8][9]. Regardless of method, the quality of the results obtained depends upon the density of scattered samples available.…”