Iterative Methods For Fixed Point Problems In Hilbert Spaces

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Iterative Methods for Fixed Point Problems in Hilbert Spaces

Author : Andrzej Cegielski
Publisher : Springer
ISBN 13 : 3642309011
Total Pages : 312 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Iterative Methods for Fixed Point Problems in Hilbert Spaces by : Andrzej Cegielski

Download or read book Iterative Methods for Fixed Point Problems in Hilbert Spaces written by Andrzej Cegielski and published by Springer. This book was released on 2012-09-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.

Iterative Methods for Sparse Linear Systems

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Iterative Methods for Solving Nonlinear Equations and Systems

Author : Juan R. Torregrosa
Publisher : MDPI
ISBN 13 : 3039219405
Total Pages : 494 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Iterative Methods for Solving Nonlinear Equations and Systems by : Juan R. Torregrosa

Download or read book Iterative Methods for Solving Nonlinear Equations and Systems written by Juan R. Torregrosa and published by MDPI. This book was released on 2019-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Iterative Approximation of Fixed Points

Author : Vasile Berinde
Publisher : Springer
ISBN 13 : 3540722343
Total Pages : 338 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Iterative Approximation of Fixed Points by : Vasile Berinde

Download or read book Iterative Approximation of Fixed Points written by Vasile Berinde and published by Springer. This book was released on 2007-04-20 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

Topics in Metric Fixed Point Theory

Author : Kazimierz Goebel
Publisher : Cambridge University Press
ISBN 13 : 9780521382892
Total Pages : 258 pages
Book Rating : 4.3/5 (828 download)

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Book Synopsis Topics in Metric Fixed Point Theory by : Kazimierz Goebel

Download or read book Topics in Metric Fixed Point Theory written by Kazimierz Goebel and published by Cambridge University Press. This book was released on 1990 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.

Approximate Solutions of Common Fixed-Point Problems

Author : Alexander J. Zaslavski
Publisher : Springer
ISBN 13 : 3319332554
Total Pages : 457 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Approximate Solutions of Common Fixed-Point Problems by : Alexander J. Zaslavski

Download or read book Approximate Solutions of Common Fixed-Point Problems written by Alexander J. Zaslavski and published by Springer. This book was released on 2016-06-30 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space“/p> · dynamic string-averaging version of the proximal algorithm · common fixed point problems in metric spaces · common fixed point problems in the spaces with distances of the Bregman type · a proximal algorithm for finding a common zero of a family of maximal monotone operators · subgradient projections algorithms for convex feasibility problems in Hilbert spaces

Approximate Fixed Points of Nonexpansive Mappings

Author : Alexander J. Zaslavski
Publisher : Springer Nature
ISBN 13 : 3031707109
Total Pages : 535 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Approximate Fixed Points of Nonexpansive Mappings by : Alexander J. Zaslavski

Download or read book Approximate Fixed Points of Nonexpansive Mappings written by Alexander J. Zaslavski and published by Springer Nature. This book was released on with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1021 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1021 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Fixed Points of Nonlinear Operators

Author : Haiyun Zhou
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110667096
Total Pages : 378 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Fixed Points of Nonlinear Operators by : Haiyun Zhou

Download or read book Fixed Points of Nonlinear Operators written by Haiyun Zhou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Methods for Fixed Points of Nonlinear Operators offers an introduction into iterative methods of fixed points for nonexpansive mappings, pseudo-contrations in Hilbert Spaces and in Banach Spaces. Iterative methods of zeros for accretive mappings in Banach Spaces and monotone mappings in Hilbert Spaces are also discussed. It is an essential work for mathematicians and graduate students in nonlinear analysis.

Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems

Author : I. Cioranescu
Publisher : Springer Science & Business Media
ISBN 13 : 9780792309109
Total Pages : 284 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems by : I. Cioranescu

Download or read book Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems written by I. Cioranescu and published by Springer Science & Business Media. This book was released on 1990-09-30 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi, ...* si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Algorithms for Solving Common Fixed Point Problems

Author : Alexander J. Zaslavski
Publisher : Springer
ISBN 13 : 3319774379
Total Pages : 320 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Algorithms for Solving Common Fixed Point Problems by : Alexander J. Zaslavski

Download or read book Algorithms for Solving Common Fixed Point Problems written by Alexander J. Zaslavski and published by Springer. This book was released on 2018-05-02 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems, the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning. Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter 4. Chapter 5 is devoted to the convergence of an abstract version of the algorithm which has been called component-averaged row projections (CARP). Chapter 6 studies a proximal algorithm for finding a common zero of a family of maximal monotone operators. Chapter 7 extends the results of Chapter 6 for a dynamic string-averaging version of the proximal algorithm. In Chapters 8 subgradient projections algorithms for convex feasibility problems are examined for infinite dimensional Hilbert spaces.

Fixed Point Theory and Graph Theory

Author : Monther Alfuraidan
Publisher : Academic Press
ISBN 13 : 0128043652
Total Pages : 444 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Fixed Point Theory and Graph Theory by : Monther Alfuraidan

Download or read book Fixed Point Theory and Graph Theory written by Monther Alfuraidan and published by Academic Press. This book was released on 2016-06-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets. - Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments - Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach - Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications

Mathematical Programs with Equilibrium Constraints

Author : Zhi-Quan Luo
Publisher : Cambridge University Press
ISBN 13 : 9780521572903
Total Pages : 432 pages
Book Rating : 4.5/5 (729 download)

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Book Synopsis Mathematical Programs with Equilibrium Constraints by : Zhi-Quan Luo

Download or read book Mathematical Programs with Equilibrium Constraints written by Zhi-Quan Luo and published by Cambridge University Press. This book was released on 1996-11-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.

Solutions of Fixed Point Problems with Computational Errors

Author : Alexander J. Zaslavski
Publisher : Springer Nature
ISBN 13 : 3031508793
Total Pages : 392 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Solutions of Fixed Point Problems with Computational Errors by : Alexander J. Zaslavski

Download or read book Solutions of Fixed Point Problems with Computational Errors written by Alexander J. Zaslavski and published by Springer Nature. This book was released on with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

From Analysis to Visualization

Author : David H. Bailey
Publisher : Springer Nature
ISBN 13 : 3030365689
Total Pages : 447 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis From Analysis to Visualization by : David H. Bailey

Download or read book From Analysis to Visualization written by David H. Bailey and published by Springer Nature. This book was released on 2020-03-16 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and researchers from all fields of mathematics are invited to read and treasure this special Proceedings. A conference was held 25 –29 September 2017 at Noah’s On the Beach, Newcastle, Australia, to commemorate the life and work of Jonathan M. Borwein, a mathematician extraordinaire whose untimely passing in August 2016 was a sorry loss to mathematics and to so many members of its community, a loss that continues to be keenly felt. A polymath, Jonathan Borwein ranks among the most wide ranging and influential mathematicians of the last 50 years, making significant contributions to an exceptional diversity of areas and substantially expanding the use of the computer as a tool of the research mathematician. The contributions in this commemorative volume probe Dr. Borwein's ongoing legacy in areas where he did some of his most outstanding work: Applied Analysis, Optimization and Convex Functions; Mathematics Education; Financial Mathematics; plus Number Theory, Special Functions and Pi, all tinged by the double prisms of Experimental Mathematics and Visualization, methodologies he championed.

Inherently Parallel Algorithms in Feasibility and Optimization and their Applications

Author : D. Butnariu
Publisher : Elsevier
ISBN 13 : 0080508766
Total Pages : 515 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Inherently Parallel Algorithms in Feasibility and Optimization and their Applications by : D. Butnariu

Download or read book Inherently Parallel Algorithms in Feasibility and Optimization and their Applications written by D. Butnariu and published by Elsevier. This book was released on 2001-06-18 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Haifa 2000 Workshop on "Inherently Parallel Algorithms for Feasibility and Optimization and their Applications" brought together top scientists in this area. The objective of the Workshop was to discuss, analyze and compare the latest developments in this fast growing field of applied mathematics and to identify topics of research which are of special interest for industrial applications and for further theoretical study.Inherently parallel algorithms, that is, computational methods which are, by their mathematical nature, parallel, have been studied in various contexts for more than fifty years. However, it was only during the last decade that they have mostly proved their practical usefulness because new generations of computers made their implementation possible in order to solve complex feasibility and optimization problems involving huge amounts of data via parallel processing. These led to an accumulation of computational experience and theoretical information and opened new and challenging questions concerning the behavior of inherently parallel algorithms for feasibility and optimization, their convergence in new environments and in circumstances in which they were not considered before their stability and reliability. Several research groups all over the world focused on these questions and it was the general feeling among scientists involved in this effort that the time has come to survey the latest progress and convey a perspective for further development and concerted scientific investigations. Thus, the editors of this volume, with the support of the Israeli Academy for Sciences and Humanities, took the initiative of organizing a Workshop intended to bring together the leading scientists in the field. The current volume is the Proceedings of the Workshop representing the discussions, debates and communications that took place. Having all that information collected in a single book will provide mathematicians and engineers interested in the theoretical and practical aspects of the inherently parallel algorithms for feasibility and optimization with a tool for determining when, where and which algorithms in this class are fit for solving specific problems, how reliable they are, how they behave and how efficient they were in previous applications. Such a tool will allow software creators to choose ways of better implementing these methods by learning from existing experience.