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Using Computer Algebra To Solve The Birkhoff Interpolation Problem
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Book Synopsis Computer Algebra in Scientific Computing by : François Boulier
Download or read book Computer Algebra in Scientific Computing written by François Boulier and published by Springer Nature. This book was released on 2020-10-17 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020, held in Linz, Austria, in September 2020. The conference was held virtually due to the COVID-19 pandemic. The 34 full papers presented together with 2 invited talks were carefully reviewed and selected from 41 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CAS in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.
Book Synopsis Some Tapas of Computer Algebra by : Arjeh M. Cohen
Download or read book Some Tapas of Computer Algebra written by Arjeh M. Cohen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.
Book Synopsis Computer Algebra Handbook by : Johannes Grabmeier
Download or read book Computer Algebra Handbook written by Johannes Grabmeier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
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.
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.
Book Synopsis Automated Deduction in Geometry by : Jürgen Richter-Gebert
Download or read book Automated Deduction in Geometry written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2001-09-12 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.
Book Synopsis Selected Papers on Algebra and Topology by Garrett Birkhoff by : J.S. Oliveira
Download or read book Selected Papers on Algebra and Topology by Garrett Birkhoff written by J.S. Oliveira and published by Springer Science & Business Media. This book was released on 1987-01-01 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume of reprints are what I consider to be my most interesting and influential papers on algebra and topology. To tie them together, and to place them in context, I have supplemented them by a series of brief essays sketching their historieal background (as I see it). In addition to these I have listed some subsequent papers by others which have further developed some of my key ideas. The papers on universal algebra, lattice theory, and general topology collected in the present volume concern ideas which have become familiar to all working mathematicians. It may be helpful to make them readily accessible in one volume. I have tried in the introduction to each part to state the most significant features of ea ch paper reprinted there, and to indieate later developments. The background that shaped and stimulated my early work on universal algebra, lattice theory, and topology may be of some interest. As a Harvard undergraduate in 1928-32, I was encouraged to do independent reading and to write an original thesis. My tutorial reading included de la Vallee-Poussin's beautiful Cours d'Analyse Infinitesimale, Hausdorff's Grundzüge der Mengenlehre, and Frechet's Espaces Abstraits. In addition, I discovered Caratheodory's 1912 paper "Vber das lineare Mass von Punktmengen" and Hausdorff's 1919 paper on "Dimension und Ausseres Mass," and derived much inspiration from them. A fragment of my thesis, analyzing axiom systems for separable metrizable spaces, was later published [2]. * This background led to the work summarized in Part IV.
Book Synopsis Numerical Solution of Elliptic Problems by : Garrett Birkhoff
Download or read book Numerical Solution of Elliptic Problems written by Garrett Birkhoff and published by SIAM. This book was released on 1984-01-01 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.
Book Synopsis Gröbner Bases and Applications by : Bruno Buchberger
Download or read book Gröbner Bases and Applications written by Bruno Buchberger and published by Cambridge University Press. This book was released on 1998-02-26 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.
Book Synopsis European Congress of Mathematics by : Carles Casacuberta
Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
Book Synopsis Computation, Cryptography, and Network Security by : Nicholas J. Daras
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.
Book Synopsis Algorithmic and Quantitative Real Algebraic Geometry by : Saugata Basu
Download or read book Algorithmic and Quantitative Real Algebraic Geometry written by Saugata Basu and published by American Mathematical Soc.. This book was released on 2003-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on ''Algorithmic and Quantitative Aspects of Real Algebraic Geometry''. Topics include deciding basic algebraic properties of real semi-algebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-algebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.
Book Synopsis Error Inequalities in Polynomial Interpolation and Their Applications by : R.P. Agarwal
Download or read book Error Inequalities in Polynomial Interpolation and Their Applications written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which presents the cumulation of the authors' research in the field, deals with Lidstone, Hermite, Abel--Gontscharoff, Birkhoff, piecewise Hermite and Lidstone, spline and Lidstone--spline interpolating problems. Explicit representations of the interpolating polynomials and associated error functions are given, as well as explicit error inequalities in various norms. Numerical illustrations are provided of the importance and sharpness of the various results obtained. Also demonstrated are the significance of these results in the theory of ordinary differential equations such as maximum principles, boundary value problems, oscillation theory, disconjugacy and disfocality. For mathematicians, numerical analysts, computer scientists and engineers.
Book Synopsis Computational Science - ICCS 2006 by :
Download or read book Computational Science - ICCS 2006 written by and published by Springer Science & Business Media. This book was released on 2006 with total page 1157 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research in Progress written by and published by . This book was released on 1971 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Methods written by G.R. Liu and published by Springer Science & Business Media. This book was released on 2007-05-26 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First International Conference on Computational Methods (ICCM04), organized by the department of Mechanical Engineering, National University of Singapore, was held in Singapore, December 15-17, 2004, with great success. This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.
Book Synopsis Numerical Analysis by : David Ronald Kincaid
Download or read book Numerical Analysis written by David Ronald Kincaid and published by American Mathematical Soc.. This book was released on 2009 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.
