Approximating scattered data with discontinuities. (English) Zbl 0823.65014

Arge, Erlend; Floater, Michael

Numer. Algorithms 8, No. 2-4, 149-166 (1994).

The aim of this paper is to present a method for approximating scattered data by a function defined on a regular two-dimensional grid. The method requires three phases: regularization, local approximation, and extrapolation. Two examples from seismic data are presented.
The method is interesting for other areas: computer aided design, terrain modelling in the mapping, industrial shape estimations in molecular modelling, and modelling of geological surfaces in oil reservoir engineering.

Reviewer: M. Gaşpar (Iaşi)

MSC:

65D10	Numerical smoothing, curve fitting
65D17	Computer-aided design (modeling of curves and surfaces)

Keywords:

scattered data approximation; regular grids; regularization; extrapolation; seismic data; computer aided design; terrain modelling; molecular modelling; geological surfaces

References:

[1]	E. Arge, M. Dæhlen and A. Tveito, Approximation of scattered data using smooth grid functions, J. Comp. Appl. Math. to appear. · Zbl 0836.65011
[2]	R. Franke and G. Nielson, Surface approximation with imposed conditions, in:Surfaces in Computer Aided Design, eds. R. Barnhill and W. Boehm (North-Holland, Amsterdam, 1983) pp. 135–146.
[3]	G.H. Golub and C.F. Van Loan,Matrix Computations (Johns Hopkins University Press, 1989). · Zbl 0733.65016
[4]	M.J.D. Powell, The theory of radial basis function approximation in 1990, in:Advances in Numerical Analysis, Vol. II, ed. W. Light (Oxford Science Publ., 1992). · Zbl 0787.65005
[5]	D. Shepard, A two-dimensional interpolation function for irregularly spaced data,Proc. 1968 ACM Nat. Conf. (1968) pp. 517–524.
[6]	G.F. Simmons,Introduction to Topology and Modern Analysis (McGraw-Hill, Tokyo, 1963). · Zbl 0105.30603