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Author: G. G. Lorentz Publisher: Cambridge University Press ISBN: 9780521302395 Category : Mathematics Languages : en Pages : 308
Book Description
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.
Author: G. G. Lorentz Publisher: Cambridge University Press ISBN: 9780521302395 Category : Mathematics Languages : en Pages : 308
Book Description
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.
Author: Ying Guang Shi Publisher: Nova Publishers ISBN: 9781590336922 Category : Mathematics Languages : en Pages : 266
Book Description
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.
Author: Rudolph A. Lorentz Publisher: Springer ISBN: 3540473009 Category : Mathematics Languages : en Pages : 200
Book Description
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.
Author: Natália Bebiano Publisher: Springer ISBN: 331949984X Category : Mathematics Languages : en Pages : 347
Book Description
This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.
Author: Amnon Jakimovski Publisher: Springer Science & Business Media ISBN: 1402041756 Category : Mathematics Languages : en Pages : 303
Book Description
This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J.L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, about the origin, tends to zero in a larger disc than the radius of convergence of the Taylor series, while each of these operators converges only in the original disc. This book will be particularly useful for researchers in approximation and interpolation theory.
Author: Rudolph A. Lorentz Publisher: Springer Science & Business Media ISBN: 9780817637101 Category : Mathematics Languages : en Pages : 606
Book Description
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.
Author: Ronald A. DeVore Publisher: Springer Science & Business Media ISBN: 9783540506270 Category : Mathematics Languages : en Pages : 468
Book Description
Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.
Author: Borislav D. Bojanov Publisher: Springer Science & Business Media ISBN: 940158169X Category : Mathematics Languages : en Pages : 287
Book Description
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.
Author: Nicholas J. Daras Publisher: Springer ISBN: 3319182757 Category : Mathematics Languages : en Pages : 754
Book Description
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.
Author: Khaled Elleithy Publisher: Springer Science & Business Media ISBN: 1402052618 Category : Technology & Engineering Languages : en Pages : 466
Book Description
The conference proceedings of: International Conference on Industrial Electronics, Technology & Automation (IETA 05) International Conference on Telecommunications and Networking (TeNe 05) International Conference on Engineering Education, Instructional Technology, Assessment, and E-learning (EIAE 05) include a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of: Industrial Electronics, Technology and Automation, Telecommunications, Networking, Engineering Education, Instructional Technology and e-Learning. The three conferences, (IETA 05, TENE 05 and EIAE 05) were part of the International Joint Conference on Computer, Information, and System Sciences, and Engineering (CISSE 2005). CISSE 2005, the World's first Engineering/Computing and Systems Research E-Conference was the first high-caliber Research Conference in the world to be completely conducted online in real-time via the internet. CISSE received 255 research paper submissions and the final program included 140 accepted papers, from more than 45 countries. The whole concept and format of CISSE 2005 was very exciting and ground-breaking. The powerpoint presentations, final paper manuscripts and time schedule for live presentations over the web had been available for 3 weeks prior to the start of the conference for all registrants, so they could pick and choose the presentations they want to attend and think about questions that they might want to ask. The live audio presentations were also recorded and are part of the permanent CISSE archive, which includes all power point presentations, papers and recorded presentations. All aspects of the conference were managed on-line; not only the reviewing, submissions and registration processes; but also the actual conference. Conference participants - authors, presenters and attendees - only needed an internet connection and sound available on their computers in order to be able to contribute and participate in this international ground-breaking conference. The on-line structure of this high-quality event allowed academic professionals and industry participants to contribute work and attend world-class technical presentations based on rigorously refereed submissions, live, without the need for investing significant travel funds or time out of the office. Suffice to say that CISSE received submissions from more than 50 countries, for whose researchers, this opportunity presented a much more affordable, dynamic and well-planned event to attend and submit their work to, versus a classic, on-the-ground conference. The CISSE conference audio room provided superb audio even over low speed internet connections, the ability to display PowerPoint presentations, and cross-platform compatibility (the conferencing software runs on Windows, Mac, and any other operating system that supports Java). In addition, the conferencing system allowed for an unlimited number of participants, which in turn granted CISSE the opportunity to allow all participants to attend all presentations, as opposed to limiting the number of available seats for each session. The implemented conferencing technology, starting with the submission & review system and ending with the online conferencing capability, allowed CISSE to conduct a very high quality, fulfilling event for all participants. See: www.cissee2005.org, sections: IETA, TENE, EIAE
Author: G. G. Lorentz
Author: G. G. Lorentz
Author: Ying Guang Shi
Author: Rudolph A. Lorentz
Author: Natália Bebiano
Author: Amnon Jakimovski
Author: Rudolph A. Lorentz
Author: Ronald A. DeVore
Author: Borislav D. Bojanov
Author: Nicholas J. Daras
Author: Khaled Elleithy