Download or read book Pade and Rational Approximation written by E.B. Safe and published by Elsevier. This book was released on 2013-05-09 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Padé and Rational Approximation: Theory and Applications presents the proceedings of the Conference on Rational Approximation with Emphasis on Applications of Padé Approximants, held in Tampa, Florida on December 15-17, 1976. The contributors focus on the interplay of theory, computation, and physical applications. This book is composed of six parts encompassing 44 chapters. The introductory part discusses the general theory of orthogonal polynomials that is the mathematical basis of Padé approximants and related matters evaluation. This text also examines the connection between approximants on a stepline in the ordinary Padé table and certain continued fractions and the convergence of diagonal Padé approximants to a class of functions with an even number of branch points. The following parts deal with the special functions and continued fractions of Padé approximation and the theory of rational approximations. These parts also investigate the geometric convergence of Chebyshev rational approximation on the half line, the optimal approximation by "Almost Classical interpolation, and the incomplete polynomials approximation. The discussion then shifts to the physical applications and computations of the Padé approximants. The concluding part presents the applications of rational approximation to gun fire control and to the White Sands Missile Range Computer Facility. This part also provides a list of some open problems and conjectures concerning polynomials and rational functions. This book is of great benefit to mathematicians, physicists, and laboratory workers.
Download or read book Extrapolation and Rational Approximation written by Claude Brezinski and published by Springer Nature. This book was released on 2020-11-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.
Download or read book Pade Approximation and Its Applications written by L. Wuytack and published by . This book was released on 2014-09-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Laurent Series and their Pad Approximations written by A. Bultheel and published by Birkhäuser. This book was released on 2012-12-06 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity.
Download or read book Rational Approximation of Real Functions written by P. P. Petrushev and published by Cambridge University Press. This book was released on 2011-03-03 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1987 book examines the approximation of real functions by real rational functions. These are a more convenient tool than polynomials, and interest in them was growing, especially after D. Newman's work in the mid-sixties. The authors present the basic achievements of the subject and also discuss some topics from complex rational approximation.
Download or read book Approximation Theory and Approximation Practice Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
Download or read book Essentials of Pad Approximants written by George A. Jr. Baker and published by Elsevier. This book was released on 1975-01-01 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essentials of Padé Approximants
Download or read book General Orthogonal Polynomials written by Herbert Stahl and published by Cambridge University Press. This book was released on 1992-04-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
Download or read book Process Control written by B. Wayne Bequette and published by Prentice Hall Professional. This book was released on 2003 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master process control hands on, through practical examples and MATLAB(R) simulations This is the first complete introduction to process control that fully integrates software tools--enabling professionals and students to master critical techniques hands on, through computer simulations based on the popular MATLAB environment. Process Control: Modeling, Design, and Simulation teaches the field's most important techniques, behaviors, and control problems through practical examples, supplemented by extensive exercises--with detailed derivations, relevant software files, and additional techniques available on a companion Web site. Coverage includes: Fundamentals of process control and instrumentation, including objectives, variables, and block diagrams Methodologies for developing dynamic models of chemical processes Dynamic behavior of linear systems: state space models, transfer function-based models, and more Feedback control; proportional, integral, and derivative (PID) controllers; and closed-loop stability analysis Frequency response analysis techniques for evaluating the robustness of control systems Improving control loop performance: internal model control (IMC), automatic tuning, gain scheduling, and enhancements to improve disturbance rejection Split-range, selective, and override strategies for switching among inputs or outputs Control loop interactions and multivariable controllers An introduction to model predictive control (MPC) Bequette walks step by step through the development of control instrumentation diagrams for an entire chemical process, reviewing common control strategies for individual unit operations, then discussing strategies for integrated systems. The book also includes 16 learning modules demonstrating how to use MATLAB and SIMULINK to solve several key control problems, ranging from robustness analyses to biochemical reactors, biomedical problems to multivariable control.
Download or read book Logarithmic Potentials with External Fields written by Edward B. Saff and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the "l/9-th" conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned "weighted" potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.
Download or read book Pade Approximation and its Applications written by L. Wuytack and published by Springer. This book was released on 2006-11-15 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pade Approximation and its Applications Amsterdam 1980 written by M.G. de Bruin and published by Springer. This book was released on 2006-12-08 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory and Applications of Numerical Analysis written by G. M. Phillips and published by Elsevier. This book was released on 1996-07-05 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. - a unique blend of theory and applications - two brand new chapters on eigenvalues and splines - inclusion of formal algorithms - numerous fully worked examples - a large number of problems, many with solutions
Download or read book Model Theory and Arithmetic written by Jean Bourgain and published by . This book was released on 1981 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book History of Continued Fractions and Pad Approximants written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...
Download or read book Pade Approximations and its Applications written by H. Werner and published by Springer. This book was released on 2006-12-08 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Econometrics written by Werner Hildenbrand and published by Cambridge University Press. This book was released on 1985-08-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes papers delivered at the Fourth World Congress of the Econometric Society. It will interest economic theorists and econometricians working in universities, government, and business and financial institutions.
