[PDF] A Generalization Of Divided Differences With Applications eBook

Author : Gheorghe Micula
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 38,6 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401153388

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The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.

Author : Claude Brezinski
Publisher : CRC Press
Page : 194 pages
File Size : 17,56 MB
Release : 2020-08-11
Category : Mathematics
ISBN : 1000147940

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This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.

Author : G. Cristescu
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 37,12 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461500036

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Lectori salutem! The kind reader opens the book that its authors would have liked to read it themselves, but it was not written yet. Then, their only choice was to write this book, to fill a gap in the mathematicalliterature. The idea of convexity has appeared in the human mind since the antiquity and its fertility has led to a huge diversity of notions and of applications. A student intending a thoroughgoing study of convexity has the sensation of swimming into an ocean. It is due to two reasons: the first one is the great number of properties and applications of the classical convexity and second one is the great number of generalisations for various purposes. As a consequence, a tendency of writing huge books guiding the reader in convexity appeared during the last twenty years (for example, the books of P. M. Gruber and J. M. Willis (1993) and R. J. Webster (1994)). Another last years' tendency is to order, from some point of view, as many convexity notions as possible (for example, the book of I. Singer (1997)). These approaches to the domain of convexity follow the previous point of view of axiomatizing it (A. Ghika (1955), W. Prenowitz (1961), D. Voiculescu (1967), V. W. Bryant and R. J. Webster (1969)). Following this last tendency, our book proposes to the reader two classifications of convexity properties for sets, both of them starting from the internal mechanism of defining them.

Author : Francesco Altomare
Publisher : Walter de Gruyter
Page : 641 pages
File Size : 34,26 MB
Release : 2011-07-21
Category : Mathematics
ISBN : 3110884585

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Author : Annette M. Bolden
Publisher :
Page : 74 pages
File Size : 32,72 MB
Release : 1998
Category : Divided differences
ISBN :

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"The main objective of this thesis project is to apply the definition of divided difference to polynomial splines. We begin by introducing different definitions of divided differences and proving their equivalence. Another main objective is to establish explicit formulas for divided differences with pairwisely distinct knots and confluent or repeated knots."--(v).