Curve and Surface Fitting With Splines
The fitting of a curve or surface through a set of observational data is a recurring problem across numerous disciplines such as applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with tensor product splines. It gives a survey of possibilities, benefits, and problems commonly confronted when approximating with this popular type of function. Dierkx demonstrates in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many theoretical and practical examples.
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algorithm approximation domain B-spline coefficients band matrix bandwidth bivariate spline boundary knots calculating computed consider contour map convex function corresponding criterion cubic spline CURFIT curve fitting data points xr data values derivative determine Dierckx efficiently equations evaluation example Figure FITPACK follows FORTRAN given graph grid interior knots interpolation IOPT iterations knot intervals knot set least-squares polynomial least-squares problem least-squares solution least-squares spline linear method minimization non-zero number of knots obtained optimal overdetermined system parameter polynomial position properties rank deficiency routine satisfied scattered data set of data set of knots simply smoothing factor smoothing function smoothing norm smoothing spline specified spherical harmonic spline approximation spline curve spline function spline surface squared residuals sum of squared surface fitting tensor product spline unit disk univariate upper triangular matrix variable vector weighted least-squares weighted sum weights wr X X X y-direction zero zq,r