Box Splines / Edition 1

by Klaus HÃllig

Overview

This book on box splines is the first book giving a complete development for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an up-to-date bibliography. It is not the book's intention to be encyclopedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis, and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. This book will be used as a supplementary text for graduate courses. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasi-interpolants and approximation power. It continues with cardinal interpolation and difference equations, approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms.

Product Details

ISBN-13:	9781441928344
Publisher:	Springer New York
Publication date:	12/03/2010
Series:	Applied Mathematical Sciences , #98
Edition description:	Softcover reprint of hardcover 1st ed. 1993
Pages:	201
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

I • Box splines defined.- II • The linear algebra of box spline spaces.- III • Quasi-interpolants & approximation power.- IV • Cardinal interpolation & difference equations.- V • Approximation by cardinal splines & wavelets.- VI • Discrete box splines & linear diophantine equations.- VII Subdivision algorithms.- References.

Editorial Reviews

Combining information previously only available in papers, the authors present basic box spline theory. Chapters discuss box splines defined, the linear algebra of box spline spaces, quasi- interpolants and approximate power, cardinal interpolation and difference equations, approximation by cardinal splines and wavelets, discrete box splines and linear diophantine equations, and subdivision algorithms. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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