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.
Download or read book Methods of Approximation Theory in Complex Analysis and Mathematical Physics written by Andrei A. Gonchar and published by . This book was released on 1992 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 1993-07-30 with total page 222 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.
Download or read book Mathematical Physics and Complex Analysis written by L. D. Faddeev and published by American Mathematical Soc.. This book was released on 1988 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of survey papers on the 50th anniversary of the institute.
Download or read book Analysis and Mathematical Physics written by Björn Gustafsson and published by Springer Science & Business Media. This book was released on 2009-10-02 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
Download or read book Introduction to Methods of Approximation in Physics and Astronomy written by Maurice H. P. M. van Putten and published by Springer. This book was released on 2017-04-07 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based on their usefulness and educational value, their applicability to a broad range of problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals an evolving universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data-analysis. The book is organized to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. Some of the topics highlighted introduce the reader to selected problems with comments on numerical methods and implementation on modern platforms including CPU-GPU computing. Developed from lectures on mathematical physics in astronomy to advanced undergraduate and beginning graduate students, this book will be a valuable guide for students and a useful reference for practicing researchers. To aid understanding, exercises are included at the end of each chapter. Furthermore, some of the exercises are tailored to introduce modern symbolic computation.
Download or read book Applications of q Calculus in Operator Theory written by Ali Aral and published by Springer Science & Business Media. This book was released on 2013-05-09 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.
Download or read book Fundamentals of Approximation Theory written by Hrushikesh Narhar Mhaskar and published by CRC Press. This book was released on 2000 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of approximation theory has become so vast that it intersects with every other branch of analysis and plays an increasingly important role in applications in the applied sciences and engineering. Fundamentals of Approximation Theory presents a systematic, in-depth treatment of some basic topics in approximation theory designed to emphasize the rich connections of the subject with other areas of study. With an approach that moves smoothly from the very concrete to more and more abstract levels, this text provides an outstanding blend of classical and abstract topics. The first five chapters present the core of information that readers need to begin research in this domain. The final three chapters the authors devote to special topics-splined functions, orthogonal polynomials, and best approximation in normed linear spaces- that illustrate how the core material applies in other contexts and expose readers to the use of complex analytic methods in approximation theory. Each chapter contains problems of varying difficulty, including some drawn from contemporary research. Perfect for an introductory graduate-level class, Fundamentals of Approximation Theory also contains enough advanced material to serve more specialized courses at the doctoral level and to interest scientists and engineers.
Download or read book Methods of Fourier Analysis and Approximation Theory written by Michael Ruzhansky and published by Birkhäuser. This book was released on 2016-03-11 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Download or read book Advances in Real and Complex Analysis with Applications written by Michael Ruzhansky and published by Birkhäuser. This book was released on 2017-10-03 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them with a number of solved examples. The topics include real and complex analysis, special functions and analytic number theory, q-series, Ramanujan’s mathematics, fractional calculus, Clifford and harmonic analysis, graph theory, complex analysis, complex dynamical systems, complex function spaces and operator theory, geometric analysis of complex manifolds, geometric function theory, Riemannian surfaces, Teichmüller spaces and Kleinian groups, engineering applications of complex analytic methods, nonlinear analysis, inequality theory, potential theory, partial differential equations, numerical analysis , fixed-point theory, variational inequality, equilibrium problems, optimization problems, stability of functional equations, and mathematical physics. It includes papers presented at the 24th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (24ICFIDCAA), held at the Anand International College of Engineering, Jaipur, 22–26 August 2016. The book is a valuable resource for researchers in real and complex analysis.
Download or read book Approximation Theory and Analytic Inequalities written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2021-07-21 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Download or read book Methods of Mathematical Physics written by Richard Courant and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.
Download or read book Approximation Theory and Methods written by M. J. D. Powell and published by Cambridge University Press. This book was released on 1981-03-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Download or read book Recent Advances in Constructive Approximation Theory written by Vijay Gupta and published by Springer. This book was released on 2018-08-10 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.
Download or read book Approximation Theory and Related Applications written by Yurii Kharkevych and published by Mdpi AG. This book was released on 2023-01-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world's leading scientists presented in this book reflect new trends in approximation theory and related topics.
Download or read book Order Stars written by A. Iserles and published by CRC Press. This book was released on 2020-11-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book familiarizes the mathematical community with an analytic tool that is capable of so many applications and presents a list of open problems which might be amenable to analysis with order stars.
