Practical Guide to Splines

Carl de Boor

358 pages, parution le 21/01/2002

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Résumé

This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters VII and VIII, while chapters IX, X, and XI are devoted to B-splines. The distances from splines with fixed and with variable knots is discussed in chapter XII. The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting. The present text version differs from the original in several respects. The book is now typeset (in plain TeX), the Fortran programs now make use of Fortran 77 features. The figures have been redrawn with the aid of Matlab, various errors have been corrected, and many more formal statements have been provided with proofs. Further, all formal statements and equations have been numbered by the same numbering system, to make it easier to find any particular item. A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series.

Contents

Preface

Polynomial Interpolation
Limitations of Polynomial Approximation
Piecewise Linear Approximation
Piecewise Cubic Interpolation
Best Approximation Properties of Complete Cubic Spline Interpolation and Its Error
Parabolic Spline Interpolation
A Representation for Piecewise Polynomial Functions
The Space II kEv and the Truncated Power Basis
The Representation of PP Functions by B-Splines
The Stable Evaluation of B-Splines and Splines
The B-Spline Series, Control Points and Knot Insertion
Local Spline Approximation and the Distance from Splines
Spline Interpolation
Smoothing and Least-Squares Approximation
The Numeral Solution of an Ordinary Differential Equation by Collocation
Taut Splines, Cardinal Splines and the Approximation of Curves
Surface Approximation by Tensor Products

Appendix

Bibliography

Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Carl de Boor
Parution	21/01/2002
Nb. de pages	358
Format	16 x 24
Couverture	Relié
Poids	656g
Intérieur	Noir et Blanc
EAN13	9780387953663
ISBN13	978-0-387-95366-3