Least squares surface approximation to scattered data using multiquadratic functions

DOI10.1007/BF02519037zbMath0831.65015MaRDI QIDQ1895902

Hans Hagen, Richard Franke, Gregory M. Nielson

Publication date: 18 February 1996

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical examplesgreedy algorithmleast squares methodscattered datasurface fittingfitting functionknot selectionmultiquadratic function

Mathematics Subject Classification ID

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

Related Items (13)

Gaussian radial basis function interpolant for the different data sites and basis centers ⋮ Application of the multiquadric method for numerical solution of elliptic partial differential equations ⋮ Implicit fitting of point cloud data using radial Hermite basis functions ⋮ Characterizing and efficiently computing quadrangulations of planar point sets ⋮ Construction of Bézier rectangles and triangles on the symmetric Dupin horn cyclide by means of inversion ⋮ A robust multiquadric method for digital elevation model construction ⋮ Dynamical knot and shape parameter setting for simulating shock wave by using multi-quadric quasi-interpolation ⋮ Interpolation by basis functions of different scales and shapes ⋮ Local hybrid approximation for scattered data fitting with bivariate splines ⋮ Normalized implicit eigenvector least squares operators for noisy scattered data: Radial basis functions ⋮ Radial basis function approximations as smoothing splines ⋮ Approximating surfaces by moving total least squares method ⋮ Geometric selection of centers for radial basis function approximations involved in intensive computer simulations

Cites Work

• Unnamed Item
• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
• Thin plate splines with tension
• Multiquadratic interpolation improved
• Some extensions of radial basis functions and their applications in artificial intelligence
• Improved accuracy of multiquadric interpolation using variable shape parameters
• Moving least squares interpolation with thin-plate splines and radial basis functions
• The parameter \(R^ 2\) in multiquadric interpolation
• A first-order blending method for triangles based upon cubic interpolation
• Scattered Data Interpolation: Tests of Some Method
• Knot Selection for Least Squares Thin Plate Splines

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