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Pade Approximation In Theoretical Physics
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Book Synopsis The Padé Approximant in Theoretical Physics by :
Download or read book The Padé Approximant in Theoretical Physics written by and published by Academic Press. This book was released on 1971-02-27 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Book Synopsis Applications Of Pade' Approximation Theory In Fluid Dynamics by : Amilcare Pozzi
Download or read book Applications Of Pade' Approximation Theory In Fluid Dynamics written by Amilcare Pozzi and published by World Scientific. This book was released on 1994-03-07 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although Padé presented his fundamental paper at the end of the last century, the studies on Padé's approximants only became significant in the second part of this century.Padé procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Padé approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction.The principal advantage of Padé approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Padé approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes.This book is divided into four parts. The first one deals with the properties of the Padé approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Padé approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Padé approximants to unsteady flows.
Book Synopsis Essentials of Padé Approximants by : George A. Jr. Baker
Download or read book Essentials of Padé 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
Book Synopsis Logarithmic Potentials with External Fields by : Edward B. Saff
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.
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.
Book Synopsis Methods of Approximation Theory in Complex Analysis and Mathematical Physics by : Andrei A. Gonchar
Download or read book Methods of Approximation Theory in Complex Analysis and Mathematical Physics written by Andrei A. Gonchar and published by Springer. This book was released on 2008-01-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. Suslov: Classical Biorthogonal Rational Functions.- V.P. Havin, A. Presa Sague: Approximation properties of harmonic vector fields and differential forms.- O.G. Parfenov: Extremal problems for Blaschke products and N-widths.- A.J. Carpenter, R.S. Varga: Some Numerical Results on Best Uniform Polynomial Approximation of x on 0,1 .- J.S. Geronimo: Polynomials Orthogonal on the Unit Circle with Random Recurrence Coefficients.- S. Khrushchev: Parameters of orthogonal polynomials.- V.N. Temlyakov: The universality of the Fibonacci cubature formulas.
Book Synopsis The Quantum Mechanical Three-Body Problem by : Erich W. Schmid
Download or read book The Quantum Mechanical Three-Body Problem written by Erich W. Schmid and published by Elsevier. This book was released on 2017-01-31 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Quantum Mechanical Three-Body Problem deals with the three-body problem in quantum mechanics. Topics include the two- and three-particle problem, the Faddeev equations and their solution, separable potentials, and variational methods. This book has eight chapters; the first of which introduces the reader to the quantum mechanical three-body problem, its difficulties, and its importance in nuclear physics. Scattering experiments with three-particle breakup are presented. Attention then turns to some concepts of quantum mechanics, with emphasis on two-particle scattering and the Hamiltonian for three particles. The chapters that follow are devoted to the Faddeev equations, including those for scattering states and transition operators, and how such equations can be solved in practice. The solution of the Faddeev equations for separable potentials and local potentials is presented, along with the use of Padé approximation to solve the Faddeev equations. This book concludes with an appraisal of variational methods for bound states, elastic and rearrangement scattering, and the breakup reaction. A promising variational method for solving the Faddeev equations is described. This book will be of value to students interested in three-particle physics and to experimentalists who want to understand better how the theoretical data are derived.
Book Synopsis Pade and Rational Approximation by : E.B. Safe
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.
Book Synopsis Advanced Mathematical Methods for Scientists and Engineers I by : Carl M. Bender
Download or read book Advanced Mathematical Methods for Scientists and Engineers I written by Carl M. Bender and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Book Synopsis Mathematical Theorems by : Lyudmila Alexeyeva
Download or read book Mathematical Theorems written by Lyudmila Alexeyeva and published by BoD – Books on Demand. This book was released on 2020-12-09 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main content of this book is related to construction of analytical solutions of differential equations and systems of mathematical physics, to development of analytical methods for solving boundary value problems for such equations and the study of properties of their solutions. A wide class of equations (elliptic, parabolic, and hyperbolic) is considered here, on the basis of which complex wave processes in biological and physical media can be simulated.The method of generalized functions presented in the book for solving boundary value problems of mathematical physics is universal for constructing solutions of boundary value problems for systems of linear differential equations with constant coefficients of any type. In the last sections of the book, the issues of calculating functions based on Padé approximations, binomial expansions, and fractal representations are considered. The book is intended for specialists in the field of mathematical and theoretical physics, mechanics and biophysics, students of mechanics, mathematics, physics and biology departments of higher educational institutions.
Book Synopsis Well-Posedness of Parabolic Difference Equations by : A. Ashyralyev
Download or read book Well-Posedness of Parabolic Difference Equations written by A. Ashyralyev and published by Birkhäuser. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.
Book Synopsis Padé Approximants: Basic theory by : George Allen Baker
Download or read book Padé Approximants: Basic theory written by George Allen Baker and published by . This book was released on 1981 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6 by : Collatz
Download or read book Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6 written by Collatz and published by Birkhäuser. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Der Band enthalt Manuskripte zu Vortragen, die auf einer von den Herausgebern geleiteten Tagung tiber "Numerische Methoden der Approximationstheorie" am Mathematischen Forschungsinstitut Ober wolfach in der Zeit vom 18.-24. Januar 1981 gehalten wurden. Das Spektrum der Vortrage reichte von der klassischen Approximations theorie tiber mehrdimensionale Approximationsverfahren bis hin zu praxisbezogenen Fragestellungen. Zu den zuerst genannten Gebieten gehorten z. B. die Verfeinerung von Fehlerabschatzungen bei der Polynominterpolation, Fragen zur Eindeutigkeit, Charakterisierung optimaler Interpolationsprozesse und Algorithmen zur rationalen Interpolation. Bei den weiteren genannten Gebieten spiegel ten zahlreiche Vortrage das steigende Interesse an der mehrdimensio nalen Interpolation, insbesondere mit verschiedenen Arten von Splines wider. Hier standen u. a. Probleme der Parameterschatzung in der Medizin und Flugtechnik, Fragen der Approximationstheorie bei der Konstruktion von Plottern und stabile Algorithmen beim Arbeiten mit mehrdimensionalen B-Splines im Mittelpunkt des Interesses. Die Tagung lieferte einen reprasentativen Ueberblick tiber die aktuellen Trends in der Approximationstheorie. Zum guten Erfolg der Tagung trug wie immer die hervorragende Be treuung durch die Mitarbeiter und Angestellten des Instituts so-' wie das verstandnisvolle Entgegenkommen des Institutsdirektors, Herrn Professor Dr. Barner, bei. Un serer besonderer Dank gilt dem Birkhauser Verlag ftir die wie stets sehr gute Ausstattung. Helmut Werner Lothar Collatz Gtinther Meinardus Hamburg Mannheim Bonn 7 INDEX Blatt, H.-P. Strenge Eindeutigkeitskonstanten und Fehlerabschatzungen bei linearer Tschebyscheff-Approximation 9 Bohmer, K. Polynom- und Spline-Interpolation (Ein Farbfilm) 26 Brannigan, M.A Multivariate Adaptive Data Fitting Algorithm 30 Brass, H. Zur numerischen Berechnung konjugierter Funktionen 43 Bultheel, A
Book Synopsis Pade Approximations and its Applications by : H. Werner
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:
Book Synopsis Parabolic Equation Methods for Electromagnetic Wave Propagation by : Mireille Levy
Download or read book Parabolic Equation Methods for Electromagnetic Wave Propagation written by Mireille Levy and published by IET. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides scientists and engineers with a tool for accurate assessment of diffraction and ducting on radio and radar systems. The author gives the mathematical background to parabolic equations modeling and describes simple parabolic equation algorithms before progressing to more advanced topics such as domain truncation, the treatment of impedance boundaries, and the implementation of very fast hybrid methods combining ray-tracing and parabolic equation techniques. The last three chapters are devoted to scattering problems, with application to propagation in urban environments and to radar-cross- section computation. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Introduction to Asymptotic Methods by : David Y. Gao
Download or read book Introduction to Asymptotic Methods written by David Y. Gao and published by CRC Press. This book was released on 2006-05-03 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Book Synopsis Practical Extrapolation Methods by : Avram Sidi
Download or read book Practical Extrapolation Methods written by Avram Sidi and published by Cambridge University Press. This book was released on 2003-06-05 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
