Interpolation of track data with radial basis methods
The authors study some interpolation problems with data sets \(S\), where \(S=\{(x_ i,y_ i),1\leq i\leq n\}\), of \(n\) distinct points in \(\mathbb{R}^ 2\), in which the points lie along tracks or paths in \(\mathbb{R}^ 2\). Four scattered data interpolation methods that perform well in a critical comparison of \textit{R. Franke} [Math. Comput. 38, 181-200 (1982; Zbl 0476.65005)] are the multiquadric method of \textit{R. L. Hardy} [Comput. Math. Appl. 19, No. 8/9, 163-208 (1990; Zbl 0692.65003)], the thin plate spline method of \textit{J. Duchon} [Lect. Notes Math. 571, 85-100 (1977; Zbl 0342.41012)], the minimum norm network method of \textit{G. M. Nielson} [Math. Comput. 40, 253-271 (1983; Zbl 0549.65005)], and the modified quadratic Shepard method of \textit{R. Franke} and \textit{G. M. Nielson} [Int. J. Numer. Methods Eng. 15, 1691-1704 (1980; Zbl 0444.65011)]. These methods are discussed and applied to several track data samples. Also, the multiquadric and thin plate spline radial basis methods are applied to various sets of data that are sampled densely along tracks in the plane.
scientific article; zbMATH DE number 150165
scientific article