Mathematical Analysis I Approximation Theory

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Mathematical Analysis, Approximation Theory and Their Applications

Themistocles M. Rassias,Vijay Gupta
Mathematical Analysis Approximation Theory and Their Applications Book PDF

Author : Themistocles M. Rassias,Vijay Gupta
Publisher : Springer
Page : 741 pages
File Size : 54,9 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9783319312811

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Mathematical Analysis, Approximation Theory and Their Applications by Themistocles M. Rassias,Vijay Gupta Pdf

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Functional Analysis and Approximation Theory in Numerical Analysis

R. S. Varga
Functional Analysis and Approximation Theory in Numerical Analysis Book PDF

Author : R. S. Varga
Publisher : SIAM
Page : 81 pages
File Size : 43,8 Mb
Release : 1971-01-01
Category : Mathematics
ISBN : 9780898710038

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Functional Analysis and Approximation Theory in Numerical Analysis by R. S. Varga Pdf

Surveys the enormous literature on numerical approximation of solutions of elliptic boundary problems by means of variational and finite element methods, requiring almost constant application of results and techniques from functional analysis and approximation theory to the field of numerical analysis.

Exploring Mathematical Analysis, Approximation Theory, and Optimization

Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos
Exploring Mathematical Analysis Approximation Theory and Optimization Book PDF

Author : Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos
Publisher : Springer Nature
Page : 474 pages
File Size : 43,6 Mb
Release : 2024-01-04
Category : Mathematics
ISBN : 9783031464874

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Exploring Mathematical Analysis, Approximation Theory, and Optimization by Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos Pdf

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.

The History of Approximation Theory

Karl-Georg Steffens
The History of Approximation Theory Book PDF

Author : Karl-Georg Steffens
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 48,5 Mb
Release : 2007-07-28
Category : Mathematics
ISBN : 9780817644758

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The History of Approximation Theory by Karl-Georg Steffens Pdf

* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation

Functional Analysis, Approximation Theory, and Numerical Analysis

John Michael Rassias
Functional Analysis Approximation Theory and Numerical Analysis Book PDF

Author : John Michael Rassias
Publisher : World Scientific
Page : 342 pages
File Size : 43,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9810207379

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Functional Analysis, Approximation Theory, and Numerical Analysis by John Michael Rassias Pdf

This book consists of papers written by outstanding mathematicians. It deals with both theoretical and applied aspects of the mathematical contributions of BANACH, ULAM, and OSTROWSKI, which broaden the horizons of Functional Analysis, Approximation Theory, and Numerical Analysis in accordance with contemporary mathematical standards.

Mathematical Analysis I: Approximation Theory

Naokant Deo,Vijay Gupta,Ana Maria Acu,P. N. Agrawal
Mathematical Analysis I Approximation Theory Book PDF

Author : Naokant Deo,Vijay Gupta,Ana Maria Acu,P. N. Agrawal
Publisher : Springer Nature
Page : 262 pages
File Size : 51,5 Mb
Release : 2020-02-17
Category : Mathematics
ISBN : 9789811511530

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Mathematical Analysis I: Approximation Theory by Naokant Deo,Vijay Gupta,Ana Maria Acu,P. N. Agrawal Pdf

This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23–25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as operator theory, approximation theory, fixed-point theory, holomorphic functions, summability theory, and analytic functions. It is a valuable resource for students as well as researchers in mathematical sciences.

Approximation Theory and Harmonic Analysis on Spheres and Balls

Feng Dai,Yuan Xu
Approximation Theory and Harmonic Analysis on Spheres and Balls Book PDF

Author : Feng Dai,Yuan Xu
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 46,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781461466604

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Approximation Theory and Harmonic Analysis on Spheres and Balls by Feng Dai,Yuan Xu Pdf

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Exploring Mathematical Analysis, Approximation Theory, and Optimization

Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos
Exploring Mathematical Analysis Approximation Theory and Optimization Book PDF

Author : Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos
Publisher : Springer
Page : 0 pages
File Size : 45,7 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 3031464869

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Exploring Mathematical Analysis, Approximation Theory, and Optimization by Nicholas J. Daras,Michael Th. Rassias,Nikolaos B. Zographopoulos Pdf

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.

Approximation Theory and Methods

M. J. D. Powell
Approximation Theory and Methods Book PDF

Author : M. J. D. Powell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 54,7 Mb
Release : 1981-03-31
Category : Mathematics
ISBN : 0521295149

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Approximation Theory and Methods by M. J. D. Powell Pdf

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.

Methods of Approximation Theory in Complex Analysis and Mathematical Physics

Andrei A. Gonchar,Edward B. Saff
Methods of Approximation Theory in Complex Analysis and Mathematical Physics Book PDF

Author : Andrei A. Gonchar,Edward B. Saff
Publisher : Springer
Page : 225 pages
File Size : 40,6 Mb
Release : 2008-01-03
Category : Mathematics
ISBN : 9783540477921

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Methods of Approximation Theory in Complex Analysis and Mathematical Physics by Andrei A. Gonchar,Edward B. Saff Pdf

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.

Multivariate Approximation Theory

E. W. Cheney
Multivariate Approximation Theory Book PDF

Author : E. W. Cheney
Publisher : SIAM
Page : 74 pages
File Size : 40,6 Mb
Release : 1986-01-01
Category : Mathematics
ISBN : 1611970199

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Multivariate Approximation Theory by E. W. Cheney Pdf

The approximation of functions of several variables continues to be a difficult problem in scientific computing because many of the algorithms required for such problems have yet to be written. This monograph is written for a broad audience of computational mathematicians and statisticians concerned with the development of algorithms or the derivation of approximations from linear projections, of which the interpolating operators are an important example. As an aid to both researchers and students, a bibliography of more than 200 titles is included.

Approximation Theory and Approximation Practice, Extended Edition

Lloyd N. Trefethen
Approximation Theory and Approximation Practice Extended Edition Book PDF

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 375 pages
File Size : 54,6 Mb
Release : 2019-01-01
Category : Mathematics
ISBN : 9781611975949

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Approximation Theory and Approximation Practice, Extended Edition by Lloyd N. Trefethen Pdf

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 field’s 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.

Approximation Theory and Algorithms for Data Analysis

Armin Iske
Approximation Theory and Algorithms for Data Analysis Book PDF

Author : Armin Iske
Publisher : Springer
Page : 358 pages
File Size : 51,6 Mb
Release : 2018-12-14
Category : Mathematics
ISBN : 9783030052287

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Approximation Theory and Algorithms for Data Analysis by Armin Iske Pdf

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.

Exact Constants in Approximation Theory

Nikolaĭ Pavlovich Korneĭchuk
Exact Constants in Approximation Theory Book PDF

Author : Nikolaĭ Pavlovich Korneĭchuk
Publisher : Cambridge University Press
Page : 472 pages
File Size : 43,5 Mb
Release : 1991-06-06
Category : Mathematics
ISBN : 0521382343

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Exact Constants in Approximation Theory by Nikolaĭ Pavlovich Korneĭchuk Pdf

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.

Approximation Theory and Spline Functions

S.P. Singh,J.H.W. Burry,B. Watson
Approximation Theory and Spline Functions Book PDF

Author : S.P. Singh,J.H.W. Burry,B. Watson
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400964662

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Approximation Theory and Spline Functions by S.P. Singh,J.H.W. Burry,B. Watson Pdf

A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22-September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including ~1ultivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invi ted speakers, whose contri butions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at MeMorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings.