Bivariate Birkhoff Interpolation

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Multivariate Birkhoff Interpolation

Author : Rudolph A. Lorentz
Publisher : Springer
ISBN 13 : 3540473009
Total Pages : 200 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Multivariate Birkhoff Interpolation by : Rudolph A. Lorentz

Download or read book Multivariate Birkhoff Interpolation written by Rudolph A. Lorentz and published by Springer. This book was released on 2006-11-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bivariate Birkhoff interpolation

Author : Rudolph A. Lorentz
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (751 download)

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Book Synopsis Bivariate Birkhoff interpolation by : Rudolph A. Lorentz

Download or read book Bivariate Birkhoff interpolation written by Rudolph A. Lorentz and published by . This book was released on 1990 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Three Papers on Bivariate Birkhoff Interpolation

Author :
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (144 download)

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Book Synopsis Three Papers on Bivariate Birkhoff Interpolation by :

Download or read book Three Papers on Bivariate Birkhoff Interpolation written by and published by . This book was released on 1986 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Three Papers on Bivariate Birkhoff Interpolation

Author : G. G. Lorentz
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (144 download)

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Book Synopsis Three Papers on Bivariate Birkhoff Interpolation by : G. G. Lorentz

Download or read book Three Papers on Bivariate Birkhoff Interpolation written by G. G. Lorentz and published by . This book was released on 1986 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Birkhoff Interpolation

Author : G. G. Lorentz
Publisher : Cambridge University Press
ISBN 13 : 9780521302395
Total Pages : 308 pages
Book Rating : 4.3/5 (23 download)

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Book Synopsis Birkhoff Interpolation by : G. G. Lorentz

Download or read book Birkhoff Interpolation written by G. G. Lorentz and published by Cambridge University Press. This book was released on 1984-12-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines.

Frontiers in Interpolation and Approximation

Author : N. K. Govil
Publisher : CRC Press
ISBN 13 : 1420011383
Total Pages : 476 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Frontiers in Interpolation and Approximation by : N. K. Govil

Download or read book Frontiers in Interpolation and Approximation written by N. K. Govil and published by CRC Press. This book was released on 2006-07-20 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.

Multivariate Splines

Author : Charles K. Chui
Publisher : SIAM
ISBN 13 : 0898712262
Total Pages : 192 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Multivariate Splines by : Charles K. Chui

Download or read book Multivariate Splines written by Charles K. Chui and published by SIAM. This book was released on 1988-01-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Topics in Multivariate Approximation

Author : C. K. Chui
Publisher : Elsevier
ISBN 13 : 1483271005
Total Pages : 346 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Topics in Multivariate Approximation by : C. K. Chui

Download or read book Topics in Multivariate Approximation written by C. K. Chui and published by Elsevier. This book was released on 2014-05-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

Approximation Theory and Functional Analysis

Author : C. K. Chui
Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Approximation Theory and Functional Analysis by : C. K. Chui

Download or read book Approximation Theory and Functional Analysis written by C. K. Chui and published by . This book was released on 1991 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume surveys the fields of approximation theory and functional analysis. Compiled in honour of G.G.Lorenz, regarded as the father of modern approximation theory, it consists of invited papers representing up-to-date research by leading mathematicians in these fields.

Mathematics from Leningrad to Austin

Author : Rudolph A. Lorentz
Publisher : Springer Science & Business Media
ISBN 13 : 9780817637101
Total Pages : 606 pages
Book Rating : 4.6/5 (371 download)

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Book Synopsis Mathematics from Leningrad to Austin by : Rudolph A. Lorentz

Download or read book Mathematics from Leningrad to Austin written by Rudolph A. Lorentz and published by Springer Science & Business Media. This book was released on 1997-07-15 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in Computational Mathematics

Author : Zhongying Chen
Publisher : CRC Press
ISBN 13 : 1000941434
Total Pages : 631 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Advances in Computational Mathematics by : Zhongying Chen

Download or read book Advances in Computational Mathematics written by Zhongying Chen and published by CRC Press. This book was released on 2023-08-25 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the refereed proceedings of the Guangzhou International Symposium on Computational Mathematics, held at the Zhongshan University, People's Republic of China. Nearly 90 international mathematicians examine numerical optimization methods, wavelet analysis, computational approximation, numerical solutions of differential and integral equations, numerical linear algebra, inverse and ill-posed problems, geometric modelling, and signal and image processing and their applications.

Theory of Birkhoff Interpolation

Author : Ying Guang Shi
Publisher : Nova Publishers
ISBN 13 : 9781590336922
Total Pages : 266 pages
Book Rating : 4.3/5 (369 download)

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Book Synopsis Theory of Birkhoff Interpolation by : Ying Guang Shi

Download or read book Theory of Birkhoff Interpolation written by Ying Guang Shi and published by Nova Publishers. This book was released on 2003 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Borislav D. Bojanov
Publisher : Springer Science & Business Media
ISBN 13 : 940158169X
Total Pages : 287 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Spline Functions and Multivariate Interpolations by : Borislav D. Bojanov

Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.

Topics in Multivariate Approximation and Interpolation

Author : Kurt Jetter
Publisher : Elsevier
ISBN 13 : 0080462049
Total Pages : 357 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Topics in Multivariate Approximation and Interpolation by : Kurt Jetter

Download or read book Topics in Multivariate Approximation and Interpolation written by Kurt Jetter and published by Elsevier. This book was released on 2005-11-15 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry. A collection of articles of highest scientific standard An excellent introduction and overview of recent topics from multivariate approximation A valuable source of references for specialists in the field A representation of the state-of-the-art in selected areas of multivariate approximation A rigorous mathematical introduction to special topics of interdisciplinary research

Rational Approximation and Interpolation

Author : P.R. Graves-Morris
Publisher : Springer
ISBN 13 : 3540391134
Total Pages : 541 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Rational Approximation and Interpolation by : P.R. Graves-Morris

Download or read book Rational Approximation and Interpolation written by P.R. Graves-Morris and published by Springer. This book was released on 2006-11-14 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lp-error Bounds for Multivariate Polynomial Interpolation Schemes

Author : Shayne Waldron
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Lp-error Bounds for Multivariate Polynomial Interpolation Schemes by : Shayne Waldron

Download or read book Lp-error Bounds for Multivariate Polynomial Interpolation Schemes written by Shayne Waldron and published by . This book was released on 1995 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013

Author : Zhixiang Yin
Publisher : Springer Science & Business Media
ISBN 13 : 3642375022
Total Pages : 1209 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013 by : Zhixiang Yin

Download or read book Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013 written by Zhixiang Yin and published by Springer Science & Business Media. This book was released on 2013-10-22 with total page 1209 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA) is one of the flagship conferences on Bio-Computing, bringing together the world’s leading scientists from different areas of Natural Computing. Since 2006, the conferences have taken place at Wuhan (2006), Zhengzhou (2007), Adelaide (2008), Beijing (2009), Liverpool & Changsha (2010), Malaysia (2011) and India (2012). Following the successes of previous events, the 8th conference is organized and hosted by Anhui University of Science and Technology in China. This conference aims to provide a high-level international forum that researchers with different backgrounds and who are working in the related areas can use to present their latest results and exchange ideas. Additionally, the growing trend in Emergent Systems has resulted in the inclusion of two other closely related fields in the BIC-TA 2013 event, namely Complex Systems and Computational Neuroscience. These proceedings are intended for researchers in the fields of Membrane Computing, Evolutionary Computing and Genetic Algorithms, DNA and Molecular Computing, Biological Computing, Swarm Intelligence, Autonomy-Oriented Computing, Cellular and Molecular Automata, Complex Systems, etc. Professor Zhixiang Yin is the Dean of the School of Science, Anhui University of Science & Technology, China. Professor Linqiang Pan is the head of the research group of Natural Computing at Huazhong University of Science and Technology, Wuhan, China. Professor Xianwen Fang also works at the Anhui University of Science & Technology.