Multidimensional Minimizing Splines

• (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.

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 Dm 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 Dm-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)