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.
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.
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.
Download or read book Total Positivity and Its Applications written by Mariano Gasca and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains both invited lectures and contributed talks presented at the meeting on Total Positivity and its Applications held at the guest house of the University of Zaragoza in Jaca, Spain, during the week of September 26-30, 1994. There were present at the meeting almost fifty researchers from fourteen countries. Their interest in thesubject of Total Positivity made for a stimulating and fruitful exchange of scientific information. Interest to participate in the meeting exceeded our expectations. Regrettably, budgetary constraints forced us to restriet the number of attendees. Professor S. Karlin, of Stanford University, who planned to attend the meeting had to cancel his participation at the last moment. Nonetheless, his almost universal spiritual presence energized and inspired all of us in Jaca. More than anyone, he influenced the content, style and quality of the presentations given at the meeting. Every article in these Proceedings (except some by Karlin hirnself) references his influential treatise Total Positivity, Volume I, Stanford University Press, 1968. Since its appearance, this book has intrigued and inspired the minds of many researchers (one of us, in his formative years, read the galley proofs and the other of us first doubted its value but then later became its totally committed disciple). All of us present at the meeting encourage Professor Karlin to return to the task of completing the anxiously awaited Volume 11 of Total Positivity.
Download or read book Computation Cryptography and Network Security written by Nicholas J. Daras and published by Springer. This book was released on 2015-09-16 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Constructive Approximation written by Ronald A. DeVore and published by Springer Science & Business Media. This book was released on 1993-11-04 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Computer Information and Systems Sciences and Engineering written by Khaled Elleithy and published by Springer Science & Business Media. This book was released on 2007-06-06 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book I J Schoenberg Selected Papers written by Boor and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Cardinal Spline Interpolation written by I. J. Schoenberg and published by SIAM. This book was released on 1973-01-01 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author explains cardinal spline functions, the basic properties of B-splines and exponential Euler splines.
Download or read book Scattered Data Approximation written by Holger Wendland and published by Cambridge University Press. This book was released on 2004-12-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations.
Download or read book Automated Deduction in Geometry written by Jürgen Richter-Gebert and published by Springer. This book was released on 2003-06-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the Third International Workshop on Automated Deduction in Geometry, ADG 2000, held in Zurich, Switzerland, in September 2000.The 16 revised full papers and two invited papers presented were carefully selected for publication during two rounds of reviewing and revision from a total of initially 31 submissions. Among the issues addressed are spatial constraint solving, automated proving of geometric inequalities, algebraic proof, semi-algebraic proofs, geometrical reasoning, computational synthetic geometry, incidence geometry, and nonstandard geometric proofs.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1973-10 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics from Leningrad to Austin Volume 2 written by Rudolph A. Lorentz and published by Springer Science & Business Media. This book was released on 1997-07-15 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: The works of George G. Lorentz, spanning more than 60 years, have played a significant role in the development and evolution of mathematical analysis. The papers presented in this volume represent a selection of his best works, along with commentary from his students and colleagues.
Download or read book Approximation Theory and Functional Analysis written by and published by Elsevier. This book was released on 1979-01-01 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation Theory and Functional Analysis
Download or read book Theory of Cryptography written by Mass.) Conference Theory of Cryptography 2004 (Cambridge and published by Springer Science & Business Media. This book was released on 2004-02-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the first International Theory of Cryptography Conference, TCC 2004, held in Cambridge, MA, USA in February 2004. The 28 revised full papers presented were carefully reviewed and selected from 70 submissions. The papers constitute a unique account of original research results on theoretical and foundational topics in cryptography; they deal with the paradigms, approaches, and techniques used to conceptualize, define, and provide solutions to natural cryptographic problems.
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.
