Exploring Mathematical Analysis Approximation Theory And Optimization

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Exploring Mathematical Analysis, Approximation Theory, and Optimization

Author : Nicholas J. Daras
Publisher : Springer Nature
ISBN 13 : 3031464877
Total Pages : 474 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Exploring Mathematical Analysis, Approximation Theory, and Optimization by : Nicholas J. Daras

Download or read book Exploring Mathematical Analysis, Approximation Theory, and Optimization written by Nicholas J. Daras and published by Springer Nature. This book was released on 2024-01-04 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Nicholas J. Daras
Publisher : Springer
ISBN 13 : 9783031464867
Total Pages : 0 pages
Book Rating : 4.4/5 (648 download)

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Book Synopsis Exploring Mathematical Analysis, Approximation Theory, and Optimization by : Nicholas J. Daras

Download or read book Exploring Mathematical Analysis, Approximation Theory, and Optimization written by Nicholas J. Daras and published by Springer. This book was released on 2023-12-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 3319312812
Total Pages : 741 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Mathematical Analysis, Approximation Theory and Their Applications by : Themistocles M. Rassias

Download or read book Mathematical Analysis, Approximation Theory and Their Applications written by Themistocles M. Rassias and published by Springer. This book was released on 2016-06-03 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : M. D. Buhmann
Publisher : Cambridge University Press
ISBN 13 : 9780521581905
Total Pages : 238 pages
Book Rating : 4.5/5 (819 download)

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Book Synopsis Approximation Theory and Optimization by : M. D. Buhmann

Download or read book Approximation Theory and Optimization written by M. D. Buhmann and published by Cambridge University Press. This book was released on 1997-11-13 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Pablo Pedregal
Publisher : Springer
ISBN 13 : 3319648438
Total Pages : 254 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Optimization and Approximation by : Pablo Pedregal

Download or read book Optimization and Approximation written by Pablo Pedregal and published by Springer. This book was released on 2017-09-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Jeffrey Humpherys
Publisher : SIAM
ISBN 13 : 1611974909
Total Pages : 709 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Foundations of Applied Mathematics, Volume I by : Jeffrey Humpherys

Download or read book Foundations of Applied Mathematics, Volume I written by Jeffrey Humpherys and published by SIAM. This book was released on 2017-07-07 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?

Convergence Estimates in Approximation Theory

Author : Vijay Gupta
Publisher : Springer Science & Business Media
ISBN 13 : 3319027654
Total Pages : 361 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Convergence Estimates in Approximation Theory by : Vijay Gupta

Download or read book Convergence Estimates in Approximation Theory written by Vijay Gupta and published by Springer Science & Business Media. This book was released on 2014-01-08 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Analysis and Approximation Theory in Numerical Analysis

Author : R. S. Varga
Publisher : SIAM
ISBN 13 : 0898710030
Total Pages : 81 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Functional Analysis and Approximation Theory in Numerical Analysis by : R. S. Varga

Download or read book Functional Analysis and Approximation Theory in Numerical Analysis written by R. S. Varga and published by SIAM. This book was released on 1971-01-01 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Mathematics and Variational Analysis

Author : Nicholas J. Daras
Publisher : Springer Nature
ISBN 13 : 3030446255
Total Pages : 564 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Computational Mathematics and Variational Analysis by : Nicholas J. Daras

Download or read book Computational Mathematics and Variational Analysis written by Nicholas J. Daras and published by Springer Nature. This book was released on 2020-06-06 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in Optimization and Approximation

Author : Ding-Zhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 1461336295
Total Pages : 402 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Advances in Optimization and Approximation by : Ding-Zhu Du

Download or read book Advances in Optimization and Approximation written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory and Applications of Iteration Methods

Author : Ioannis K. Argyros
Publisher : CRC Press
ISBN 13 : 1000536750
Total Pages : 470 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis The Theory and Applications of Iteration Methods by : Ioannis K. Argyros

Download or read book The Theory and Applications of Iteration Methods written by Ioannis K. Argyros and published by CRC Press. This book was released on 2022-01-21 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Approximation and Optimization

Author : Ioannis C. Demetriou
Publisher : Springer
ISBN 13 : 3030127672
Total Pages : 237 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Approximation and Optimization by : Ioannis C. Demetriou

Download or read book Approximation and Optimization written by Ioannis C. Demetriou and published by Springer. This book was released on 2019-05-10 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Applied Mathematics, Volume 2

Author : Jeffrey Humpherys
Publisher : SIAM
ISBN 13 : 1611976065
Total Pages : 806 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Foundations of Applied Mathematics, Volume 2 by : Jeffrey Humpherys

Download or read book Foundations of Applied Mathematics, Volume 2 written by Jeffrey Humpherys and published by SIAM. This book was released on 2020-03-10 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization—essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built. This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximation, including Fourier series, wavelets, and polynomial approximation; and the theory and practice of optimization, including dynamic optimization. When used in concert with the free supplemental lab materials, Foundations of Applied Mathematics, Volume 2: Algorithms, Approximation, Optimization teaches not only the theory but also the computational practice of modern mathematical methods. Exercises and examples build upon each other in a way that continually reinforces previous ideas, allowing students to retain learned concepts while achieving a greater depth. The mathematically rigorous lab content guides students to technical proficiency and answers the age-old question “When am I going to use this?” This textbook is geared toward advanced undergraduate and beginning graduate students in mathematics, data science, and machine learning.

Linear Optimization and Approximation

Author : K. Glashoff
Publisher : Springer Science & Business Media
ISBN 13 : 1461211425
Total Pages : 209 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Linear Optimization and Approximation by : K. Glashoff

Download or read book Linear Optimization and Approximation written by K. Glashoff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Approximation and Computation in Science and Engineering

Author : Nicholas J. Daras
Publisher : Springer
ISBN 13 : 9783030841249
Total Pages : 0 pages
Book Rating : 4.8/5 (412 download)

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Book Synopsis Approximation and Computation in Science and Engineering by : Nicholas J. Daras

Download or read book Approximation and Computation in Science and Engineering written by Nicholas J. Daras and published by Springer. This book was released on 2023-05-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Real Analysis

Author : Emmanuele DiBenedetto
Publisher : Birkhäuser
ISBN 13 : 1493940058
Total Pages : 596 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Real Analysis by : Emmanuele DiBenedetto

Download or read book Real Analysis written by Emmanuele DiBenedetto and published by Birkhäuser. This book was released on 2016-09-17 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Recent Trends in Optimization Theory and Applications

Author : Ratan Prakash Agarwal
Publisher : World Scientific
ISBN 13 : 9789810223823
Total Pages : 506 pages
Book Rating : 4.2/5 (238 download)

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Book Synopsis Recent Trends in Optimization Theory and Applications by : Ratan Prakash Agarwal

Download or read book Recent Trends in Optimization Theory and Applications written by Ratan Prakash Agarwal and published by World Scientific. This book was released on 1995 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. This volume contains 30 research articles on the theory of optimization and its applications by the leading scientists in the field. It is hoped that the material in the present volume will open new vistas in research.Contributors: B D O Anderson, M Bertaja, O J Boxma, O Burdakov, A Cantoni, D J Clements, B D Craven, J B Cruz, Jr., P Diamond, S V Drakunov, Y G Evtushenko, N M Filatov, I Galligani, J C Geromel, F Giannessi, M J Grimble, G O Guardabassi, D-W Gu, C H Houpis, D G Hull, C Itiki, X Jian, M A Johnson, R E Kalaba, J C Kalkkuhl, M R Katebi, T J Kim, P Kloeden, T Kobylarz, A J Laub, C S Lee, G Leitmann, B-G Liu, J Liu, Z-Q Luo, K A Lurie, P Maponi, J B Matson, A Mess, G Pacelli, M Pachter, I Postlethwaite, T Rapcsak, M C Recchioni, Y Sakawa, S V Savastyuk, K Schittkowski, Y Shi, M A Sikora, D D Siljak, K L Teo, C Tovey, P Tseng, F E Udwadia, H Unbehauen, A Vladimirov, B Vo, J F Whidborne, R Xu, P L Yu, V G Zhadan, F Zirilli.