Multidimensional Minimizing Splines: Theory and Applications / Edition 1

by R. Arcangïli, Marïa Cruz Lïpez de Silanes, Juan Josï Torrens

Overview

This book is of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods. From reviews: The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005).

Product Details

ISBN-13:	9781402077869
Publisher:	Springer US
Publication date:	06/24/2004
Edition description:	2004
Pages:	263
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

(m, s)-Splines.- The spaces Xm, s.- Interpolating (m, s)-Splines.- Smoothing (m, s)-Splines.- (m,l,s)-Splines.- Dm-Splines Over a Bounded Domain of—n.- Dm-Splines Over—.- Discrete Dm-Splines.- Univariate Dm-Splines.- Applications of Discrete Dm-Splines.- Construction of Explicit Surfaces from Large Data Sets.- Approximation of Faulted Explicit Surfaces.- Fitting an Explicit Surface Along a Set of Curves.- Fitting an Explicit Surface Over an Open Set.- Approximation of Parametric Surfaces.

Editorial Reviews

From the reviews:

"Part of the purpose of this book is to describe an abstract theory of minimizing splines which includes the Duchon splines … . Four chapters are devoted to this subject. … The rest of the book deals with what are called discrete D^m splines. … These chapters contain explicit examples with tables giving numerical results … . The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005)

"This book is devoted to the theory of multivariate minimizing splines and some applications in surface approximation. It is mainly written for postgraduates. … This well-written book is divided into 3 parts. Part A presents the theory of (m,s)-splines over Rⁿ. … In Part B, the authors treat D^m-splines over a bounded domain … . Finally, Part C discusses some applications in geophysics and geology arising in oil research." (Manfred Tasche, Zentralblatt MATH, Vol. 1064 (15), 2005)

From the Publisher