A Modified Local Distance-weighted (MLD) Method of Interpolation and Its Numerical Performances for Large Scattered Datasets

Abstract

The purpose of this study was to propose a new interpolation scheme that was designed to remedy the shortcomings encountered in two popular interpolation methods; the triangle-based blending (TBB) method and the inverse distance weighted (IDW) method. At the same time, the proposed method combines their desirable aspects, which are the local nature and non-use of quadratic surface construction, making it comparatively less time-consuming and more independent of the global effect. Because of these properties, the new scheme was named the ‘Modified Local Distance-Weighted (MLD)’ method, and it was tested in detail with different sizes of datasets. The datasets involved in this investigation were of two types; uniformly and non-uniformly distributed. The performances were carefully monitored and assessed via several criteria; accuracy, sensitivity to parameters, CPU-time, storage requirement and ease of implementation. For comparative purposes, three alternative interpolation methods were simultaneously carried out, i.e. TBB, IDW and Radial Basis Function-Based (RBF) method. The investigation clearly revealed promising aspects of the proposed scheme where a good quality of results was anticipated, and CPU-time and storage were seen to have been significantly reduced. The research strongly indicates the benefits of the proposed method for larger sized datasets for real practical scientific and engineering uses in the future.

ON A LOCAL $k$-POINT MULTIQUADRIC NEURAL NETWORK IN FUNCTION RECOVERY APPLICATIONS

“…Secondly, it is still sceptical whether or not including all information from all interpolation nodes can guarantee better solutions. To remedy all these, some nice numerical strategies can be found in [19][20][21][22].…”

“…Some successful applications are those for function approximation [8], for solving the regulator equations [9], for classifying weblog dataset [10], for support vector machine classifiers [11], for numerically solving partial differential equations [12,13], and that with an adaptive algorithm [14]. In addition, applications of RBFs-neural networks under the context of pattern recognition and data dimensionality reduction have recently and successfully been documented in [15][16][17].…”