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Nonlinear Numerical Methods And Rational Approximation
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Book Synopsis Nonlinear Numerical Methods and Rational Approximation by : A. Cuyt
Download or read book Nonlinear Numerical Methods and Rational Approximation written by A. Cuyt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; use Stein spaces. And in addition to this there are and prediction and electrical engineering can such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Nonlinear Methods in Numerical Analysis by : A. Cuyt
Download or read book Nonlinear Methods in Numerical Analysis written by A. Cuyt and published by Elsevier. This book was released on 1987-03-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.
Book Synopsis Nonlinear Numerical Methods and Rational Approximation II by : A. Cuyt
Download or read book Nonlinear Numerical Methods and Rational Approximation II written by A. Cuyt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the international conference on "Nonlinear numerical methods and Rational approximation II" organised by Annie Cuyt at the University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70's. The following figures illustrate the growing number of participants and their geographical dissemination. In 1993 the Belgian scientific committee consisted of A. Bultheel (Leuven), A. Cuyt (Antwerp), J. Meinguet (Louvain-Ia-Neuve) and J.-P. Thiran (Namur). The conference focused on the use of rational functions in different fields of Numer ical Analysis. The invited speakers discussed "Orthogonal polynomials" (D. S. Lu binsky), "Rational interpolation" (M. Gutknecht), "Rational approximation" (E. B. Saff) , "Pade approximation" (A. Gonchar) and "Continued fractions" (W. B. Jones). In contributed talks multivariate and multidimensional problems, applications and implementations of each main topic were considered. To each of the five main topics a separate conference day was devoted and a separate proceedings chapter compiled accordingly. In this way the proceedings reflect the organisation of the talks at the conference. Nonlinear numerical methods and rational approximation may be a nar row field for the outside world, but it provides a vast playground for the chosen ones. It can fascinate specialists from Moscow to South-Africa, from Boulder in Colorado and from sunny Florida to Zurich in Switzerland.
Book Synopsis Nonlinear Approximation Theory by : Dietrich Braess
Download or read book Nonlinear Approximation Theory written by Dietrich Braess and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approxima tion is strongly connected with his name. By making use of his ideas, the theories of best uniform approximation by rational functions and by polynomials were developed over the years in an almost unified framework. The difference between linear and rational approximation and its implications first became apparent in the 1960's. At roughly the same time other approaches to nonlinear approximation were also developed. The use of new tools, such as nonlinear functional analysis and topological methods, showed that linearization is not sufficient for a complete treatment of nonlinear families. In particular, the application of global analysis and the consideration of flows on the family of approximating functions intro duced ideas which were previously unknown in approximation theory. These were and still are important in many branches of analysis. On the other hand, methods developed for nonlinear approximation prob lems can often be successfully applied to problems which belong to or arise from linear approximation. An important example is the solution of moment problems via rational approximation. Best quadrature formulae or the search for best linear spaces often leads to the consideration of spline functions with free nodes. The most famous problem of this kind, namely best interpolation by poly nomials, is treated in the appendix of this book.
Book Synopsis Mathematical Constants by : Steven R. Finch
Download or read book Mathematical Constants written by Steven R. Finch and published by Cambridge University Press. This book was released on 2003-08-18 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Book Synopsis Biorthogonality and its Applications to Numerical Analysis by : Claude Brezinski
Download or read book Biorthogonality and its Applications to Numerical Analysis written by Claude Brezinski and published by CRC Press. This book was released on 2020-08-11 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.
Book Synopsis Computational Methods And Function Theory 1994 - Proceedings Of The Conference by : R M Ali
Download or read book Computational Methods And Function Theory 1994 - Proceedings Of The Conference written by R M Ali and published by World Scientific. This book was released on 1995-10-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics discussed at the conference revolved around the interaction of computational methods and theoretical function theory, as well as recent advances and developments in both fields. The talks ranged from analytic function theory to approximation theory to numerical conformal mapping and other computational methods.
Book Synopsis Pade Approximants by : George Allen Baker
Download or read book Pade Approximants written by George Allen Baker and published by Cambridge University Press. This book was released on 1996-01-26 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book was reviewed in 1982 as "the most extensive treatment of Pade approximants actually available." This second edition has been thoroughly updated, with a substantial new chapter on multiseries approximants. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, and computational methods. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1970 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Analysis: Historical Developments in the 20th Century by : C. Brezinski
Download or read book Numerical Analysis: Historical Developments in the 20th Century written by C. Brezinski and published by Elsevier. This book was released on 2012-12-02 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.
Book Synopsis Orthogonal Polynomials and Their Applications by : Jaime Vinuesa
Download or read book Orthogonal Polynomials and Their Applications written by Jaime Vinuesa and published by CRC Press. This book was released on 1989-05-25 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Orthogonal Functions by : William Jones
Download or read book Orthogonal Functions written by William Jones and published by CRC Press. This book was released on 2020-12-22 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."
Book Synopsis Progress in Industrial Mathematics at ECMI 2010 by : Michael Günther
Download or read book Progress in Industrial Mathematics at ECMI 2010 written by Michael Günther and published by Springer Science & Business Media. This book was released on 2012-04-05 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: ECMI, the European Consortium for Mathematics in Industry, is the European brand associated with applied mathematics for industry and organizes highly successful biannual conferences. In this series, the ECMI 2010, the 16th European Conference on Mathematics for Industry, was held in the historic city hall of Wuppertal in Germany. It covered the mathematics of a wide range of applications and methods, from circuit and electromagnetic device simulation to model order reduction for chip design, uncertainties and stochastics, production, fluids, life and environmental sciences, and dedicated and versatile methods. These proceedings of ECMI 2010 emphasize mathematics as an innovation enabler for industry and business, and as an absolutely essential pre-requiste for Europe on its way to becoming the leading knowledge-based economy in the world.
Book Synopsis Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions by : Thomas Trogdon
Download or read book Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions written by Thomas Trogdon and published by SIAM. This book was released on 2015-12-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.?
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Krylov Methods for Nonsymmetric Linear Systems by : Gérard Meurant
Download or read book Krylov Methods for Nonsymmetric Linear Systems written by Gérard Meurant and published by Springer Nature. This book was released on 2020-10-02 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.
