Practical Guide to Splines Applied Mathematical Sciences 27

Carl De Boor

ISBN 10: 0387903569 / ISBN 13: 9780387903569

Verlag: Springer-Verlag, New York, 1978

Beschreibung

Covers have minor wear, bumping and soil. Corners and ends of spline bumped and rubbed. Binding tight. No writing. xxiv + 392 pages including appendix and index. Discusses polynomial splines as linear combinations of B-splines and provides proofs for some of the results and offers many Fortran programs useful in calculations. Size: 6.25 x 9.25. Bestandsnummer des Verkäufers 039926

Bibliografische Details

Titel: Practical Guide to Splines Applied ...

Verlag: Springer-Verlag, New York

Erscheinungsdatum: 1978

Einband: Paperback

Zustand: Good

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Inhaltsangabe:

Book by Boor Carl de

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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.