Exploring Mathematical Analysis Approximation Theory And Optimization

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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 : 46,9 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.

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 : 50,7 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.

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 : 51,9 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.

Approximation Theory and Optimization

M. D. Buhmann,A. Iserles
Approximation Theory and Optimization Book PDF

Author : M. D. Buhmann,A. Iserles
Publisher : Cambridge University Press
Page : 238 pages
File Size : 47,9 Mb
Release : 1997-11-13
Category : Mathematics
ISBN : 0521581907

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Approximation Theory and Optimization by M. D. Buhmann,A. Iserles Pdf

Michael Powell is one of the world's foremost figures in numerical analysis. This volume, first published in 1997, is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell's own achievements, focuses on innovative work in optimisation and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys. They have all been reviewed and edited to form a coherent volume for this important discipline within mathematics, with highly relevant applications throughout science and engineering.

Optimization and Approximation

Pablo Pedregal
Optimization and Approximation Book PDF

Author : Pablo Pedregal
Publisher : Springer
Page : 254 pages
File Size : 45,8 Mb
Release : 2017-09-07
Category : Mathematics
ISBN : 9783319648439

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Optimization and Approximation by Pablo Pedregal Pdf

This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

Foundations of Applied Mathematics, Volume I

Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
Foundations of Applied Mathematics Volume I Book PDF

Author : Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
Publisher : SIAM
Page : 709 pages
File Size : 54,7 Mb
Release : 2017-07-07
Category : Mathematics
ISBN : 9781611974904

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Foundations of Applied Mathematics, Volume I by Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans Pdf

This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis?includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?

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 : 45,9 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.

Convergence Estimates in Approximation Theory

Vijay Gupta,Ravi P. Agarwal
Convergence Estimates in Approximation Theory Book PDF

Author : Vijay Gupta,Ravi P. Agarwal
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 54,5 Mb
Release : 2014-01-08
Category : Mathematics
ISBN : 9783319027654

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Convergence Estimates in Approximation Theory by Vijay Gupta,Ravi P. Agarwal Pdf

The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.

Linear Optimization and Approximation

K. Glashoff,S.-A. Gustafson
Linear Optimization and Approximation Book PDF

Author : K. Glashoff,S.-A. Gustafson
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461211426

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Linear Optimization and Approximation by K. Glashoff,S.-A. Gustafson Pdf

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Real Analysis

Emmanuele DiBenedetto
Real Analysis Book PDF

Author : Emmanuele DiBenedetto
Publisher : Birkhäuser
Page : 596 pages
File Size : 53,9 Mb
Release : 2016-09-17
Category : Mathematics
ISBN : 9781493940059

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Real Analysis by Emmanuele DiBenedetto Pdf

The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a “Problems and Complements” section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts. The first eight chapters explore all of the basic topics for training in real analysis, beginning with a review of countable sets before moving on to detailed discussions of measure theory, Lebesgue integration, Banach spaces, functional analysis, and weakly differentiable functions. More topical applications are discussed in the remaining chapters, such as maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions. This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces. Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both for students discovering real analysis for the first time and for mathematicians and researchers looking for a useful resource for reference or review. Praise for the First Edition: “[This book] will be extremely useful as a text. There is certainly enough material for a year-long graduate course, but judicious selection would make it possible to use this most appealing book in a one-semester course for well-prepared students.” —Mathematical Reviews

Computational Mathematics and Variational Analysis

Nicholas J. Daras,Themistocles M. Rassias
Computational Mathematics and Variational Analysis Book PDF

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer Nature
Page : 564 pages
File Size : 44,8 Mb
Release : 2020-06-06
Category : Mathematics
ISBN : 9783030446253

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Computational Mathematics and Variational Analysis by Nicholas J. Daras,Themistocles M. Rassias Pdf

This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inner product spaces, function variation principles and normed minimizers, equilibria of parametrized N-player nonlinear games, multi-symplectic numerical schemes for differential equations, time-delay multi-agent systems, computational methods in non-linear design of experiments, unsupervised stochastic learning, asymptotic statistical results, global-local transformation, scattering relations of elastic waves, generalized Ostrowski and trapezoid type rules, numerical approximation, Szász Durrmeyer operators and approximation, integral inequalities, behaviour of the solutions of functional equations, functional inequalities in complex Banach spaces, functional contractions in metric spaces.

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 : 44,9 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 and Optimization

Ioannis C. Demetriou,Panos M. Pardalos
Approximation and Optimization Book PDF

Author : Ioannis C. Demetriou,Panos M. Pardalos
Publisher : Springer
Page : 237 pages
File Size : 43,5 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9783030127671

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Approximation and Optimization by Ioannis C. Demetriou,Panos M. Pardalos Pdf

This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.

The Theory and Applications of Iteration Methods

Ioannis K. Argyros
The Theory and Applications of Iteration Methods Book PDF

Author : Ioannis K. Argyros
Publisher : CRC Press
Page : 470 pages
File Size : 46,7 Mb
Release : 2022-01-21
Category : Mathematics
ISBN : 9781000536751

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The Theory and Applications of Iteration Methods by Ioannis K. Argyros Pdf

The theory and applications of Iteration Methods is a very fast-developing field of numerical analysis and computer methods. The second edition is completely updated and continues to present the state-of-the-art contemporary theory of iteration methods with practical applications, exercises, case studies, and examples of where and how they can be used. The Theory and Applications of Iteration Methods, Second Edition includes newly developed iteration methods taking advantage of the most recent technology (computers, robots, machines). It extends the applicability of well-established methods by increasing the convergence domain and offers sharper error tolerance. New proofs and ideas for handling convergence are introduced along with a new variety of story problems picked from diverse disciplines. This new edition is for researchers, practitioners, and students in engineering, economics, and computational sciences.

Advances in Optimization and Approximation

Ding-Zhu Du,Jie Sun
Advances in Optimization and Approximation Book PDF

Author : Ding-Zhu Du,Jie Sun
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 46,8 Mb
Release : 1994-05-31
Category : Business & Economics
ISBN : UOM:39015032550157

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Advances in Optimization and Approximation by Ding-Zhu Du,Jie Sun Pdf

This book is a collection of research papers in optimization and approximation dedicated to Professor Minyi Yue of the Institute of Applied Mathematics, Beijing, China. The papers provide a broad spectrum of research on optimization problems, including scheduling, location, assignment, linear and nonlinear programming problems as well as problems in molecular biology. The emphasis of the book is on algorithmic aspects of research work in optimization. Special attention is paid to approximation algorithms, including heuristics for combinatorial approximation problems, approximation algorithms for global optimization problems, and applications of approximations in real problems. The work provides the state of the art for researchers in mathematical programming, operations research, theoretical computer science and applied mathematics.