Multivariate Birkhoff Interpolation
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Multivariate Birkhoff Interpolation
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Author : Rudolph A. Lorentz
language : en
Publisher: Springer
Release Date : 2006-11-15
Multivariate Birkhoff Interpolation written by Rudolph A. Lorentz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well as a chapter with formulas for Vandermonde determinants. Finally, the technique is applied to non-standard interpolations. The book is principally oriented to specialists in the field. However, since all the proofs are presented in full detail and since examples are profuse, a wider audience with a basic knowledge of analysis and linear algebra will draw profit from it. Indeed, the fundamental nature of multivariate nature of multivariate interpolation is reflected by the fact that readers coming from the disparate fields of algebraic geometry (singularities of surfaces), of finite elements and of CAGD will also all find useful information here.
Theory Of Birkhoff Interpolation
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Author : Ying Guang Shi
language : en
Publisher: Nova Publishers
Release Date : 2003
Theory Of Birkhoff Interpolation written by Ying Guang Shi and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Interpolation by polynomials is a very old subject. The first systematic work was due to Newton in the seventeenth century. Lagrange developed his formula only a little later. In 1878 Hermie introduced so called Hermite interpolation. In 1906 Birkhoff published the first paper on lacunary (or Birkhoff) interpolation whose information about a function and its derivatives is irregular. It turns out that the Birkhoff interpolation problem is very difficult. The reasons are: the solvability of the problem is equivalent to non-singularity of the coefficient matrix of higher order, which of course is not easy to determine in general; should the solvability of the problem be known, it is difficult to get an explicit representation of the solution; although an explicit representation of the solution in some special cases can be acquired, it is usually complicated and is hard to study. This book is largely self-contained. It begins with the definitions and elementary properties of Birkhoff interpolation, to be followed by the formulating of the fundamental theorems for regularity and comparison theorems; also investigated are fundamental polynomials of interpolation in details. Interpolation follow.
Spline Functions And Multivariate Interpolations
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Author : Borislav D. Bojanov
language : en
Publisher: Springer
Release Date : 1993-03-31
Spline Functions And Multivariate Interpolations written by Borislav D. Bojanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-31 with Computers categories.
This volume provides a comprehensive introduction to the theory of spline functions. Emphasis is given to new developments, such as the general Birkhoff-type interpolation, the extremal properties of splines, their prominent role in the optimal recovery of functions, and multivariate interpolation by polynomials and splines. The book has thirteen chapters dealing, respectively, with interpolation by algebraic polynomials, the space of splines, B-splines, interpolation by spline functions, natural spline functions, perfect splines, monosplines, periodic splines, multivariate B-splines and truncated powers, multivariate spline functions and divided differences, box splines, multivariate mean value interpolation, multivariate polynomial interpolations arising by hyperplanes, and multivariate pointwise interpolation. Some of the results described are presented as exercises and hints are given for their solution. For researchers and graduate students whose work involves approximation theory.
Computation Cryptography And Network Security
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Author : Nicholas J. Daras
language : en
Publisher: Springer
Release Date : 2015-09-16
Computation Cryptography And Network Security written by Nicholas J. Daras and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-16 with Mathematics categories.
Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy, and brings together a broad variety of mathematical methods and theories with several applications. It discusses directions and pursuits of scientists that pertain to engineering sciences. It is also presents the theoretical background required for algorithms and techniques applied to a large variety of concrete problems. A number of open questions as well as new future areas are also highlighted. This book will appeal to operations research analysts, engineers, community decision makers, academics, the military community, practitioners sharing the current “state-of-the-art,” and analysts from coalition partners. Topics covered include Operations Research, Games and Control Theory, Computational Number Theory and Information Security, Scientific Computing and Applications, Statistical Modeling and Applications, Systems of Monitoring and Spatial Analysis.
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Author : 崔凯
language : zh-CN
Publisher: 重庆大学电子音像出版社有限公司
Release Date : 2023-05-01
written by 崔凯 and has been published by 重庆大学电子音像出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-01 with Mathematics categories.
本书主要总结了作者近年来在多元非理想插值方面的相关工作，主要包括以下三方面的研究成果：提出了更一般的多元插值格式，得到了插值格式几乎正则的一个必要条件和正则的一个充分条件；将单项微分插值条件的插值问题拓展到了多项式微分插值条件的情形，并将计算理想插值的BM算法推广到了多元非理想插值问题上；给定摄动结点集，得到了计算任意单项序下稳定单项基的算法，并将该算法应用在曲面重建中。
Mathematics From Leningrad To Austin
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Author : Rudolph A. Lorentz
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-15
Mathematics From Leningrad To Austin written by Rudolph A. Lorentz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-15 with Mathematics categories.
This "Select a" contains approximately two thirds of the papers my 1932 to 1994. These papers are divided into four fields. father wrote from The first volume contains the papers on 1) Summability and Number Theory and 2) Interpolation. The second volume contains the fields 3) Real and Functional Analysis and 4) Approximation Theory. Each of these four groups of papers is introduced by a review of the contents and significance, respectively of the impact of these papers. The first volume contains, in addition, an autobiography, a complete list of publications, a list of doctoral students and four unpublished essays on mathematics in general: a) A report on the University of Leningrad b) On the work of the mathematical mind c) Proofs in Mathematics d) About Mathematical books. The report on the University of Leningrad, written in the late '40's, is a unique historical document which is still of current interest for several reasons. It is of interest for professional reasons since it contains a com plete description of a mathematics majors' curriculum through his entire course of studies. From it one can see both the changes and invariants of course material as well as the students' course load. Then one can also see the consequences of admittedly extreme political intervention in uni versity affairs. Today we use the term "politically correct", but in those times being politically correct was a matter of life and death.
Rational Approximation And Interpolation
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Author : P.R. Graves-Morris
language : en
Publisher: Springer
Release Date : 2006-11-14
Rational Approximation And Interpolation written by P.R. Graves-Morris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Approximation Theory Wavelets And Applications
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Author : S.P. Singh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Approximation Theory Wavelets And Applications written by S.P. Singh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.
Gr Bner Bases And Applications
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Author : Bruno Buchberger
language : en
Publisher: Cambridge University Press
Release Date : 1998-02-26
Gr Bner Bases And Applications written by Bruno Buchberger and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-26 with Mathematics categories.
Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.
Analysis And Applications
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Author : H. P. Dikshit
language : en
Publisher: CRC Press
Release Date : 2003-01-29
Analysis And Applications written by H. P. Dikshit and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-29 with Mathematics categories.
Analysis and its applications have been major areas for research in mathematics and allied fields. The fast growing power of computation has made a significant and useful impact in these areas. This has lead to computational analysis and the emergence of fields like Bezier-Bernstein methods for computer-aided geometric design, constructive approximation and wavelets, and even computational harmonic analysis. Analysis and Applications consists of research articles, including a few survey articles, by eminent mathematicians projecting trends in constructive and computational approximation, summability theory, optimal control and theory and applications of function spaces and wavelets.