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Arcangeli R., De Silanes M.C.L., Torrens J.J. Multidimensional Minimizing Splines: Theory and Applications

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Arcangeli R., De Silanes M.C.L., Torrens J.J. Multidimensional Minimizing Splines: Theory and Applications
Springer, 2004. – 280 p. – ISBN: 1402077866, 9781402077869
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.
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)
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