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Author: Rolando Gárciga Otero
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We introduce in this paper a new class of nonlinear operators which contains, among others, the class of operators with semimonotone additive inverse and also the class of nonexpansive mappings. We study this class and discuss some of its properties. Then we present iterative procedures for computing fixed points of operators in this class, which allow for inexact solutions of the subproblems and relative error criteria. We prove weak convergence of the generated sequences in the context of Hilbert spaces. Strong convergence is also discussed.
Author: Rolando Gárciga Otero
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We introduce in this paper a new class of nonlinear operators which contains, among others, the class of operators with semimonotone additive inverse and also the class of nonexpansive mappings. We study this class and discuss some of its properties. Then we present iterative procedures for computing fixed points of operators in this class, which allow for inexact solutions of the subproblems and relative error criteria. We prove weak convergence of the generated sequences in the context of Hilbert spaces. Strong convergence is also discussed.
Author: Andrzej Cegielski
Publisher: Springer
ISBN: 3642309011
Category : Mathematics
Languages : en
Pages : 312
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Book Description
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.
Author: A. F. Leont'Ev
Publisher: American Mathematical Soc.
ISBN: 9780821817100
Category :
Languages : en
Pages : 418
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Book Description
Author: Vasile Berinde
Publisher: Springer
ISBN: 3540722343
Category : Mathematics
Languages : en
Pages : 338
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Book Description
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.
Author: Vittorino Pata
Publisher: Springer Nature
ISBN: 3030196704
Category : Mathematics
Languages : en
Pages : 171
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Book Description
This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.
Author: Ioannis K Argyros
Publisher: World Scientific Publishing Company
ISBN: 9813106549
Category : Mathematics
Languages : en
Pages : 527
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Book Description
Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.
Author: Michael Ruzhansky
Publisher: Birkhäuser
ISBN: 981104337X
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them with a number of solved examples. The topics include real and complex analysis, special functions and analytic number theory, q-series, Ramanujan’s mathematics, fractional calculus, Clifford and harmonic analysis, graph theory, complex analysis, complex dynamical systems, complex function spaces and operator theory, geometric analysis of complex manifolds, geometric function theory, Riemannian surfaces, Teichmüller spaces and Kleinian groups, engineering applications of complex analytic methods, nonlinear analysis, inequality theory, potential theory, partial differential equations, numerical analysis , fixed-point theory, variational inequality, equilibrium problems, optimization problems, stability of functional equations, and mathematical physics. It includes papers presented at the 24th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (24ICFIDCAA), held at the Anand International College of Engineering, Jaipur, 22–26 August 2016. The book is a valuable resource for researchers in real and complex analysis.
Author: Heinz H. Bauschke
Publisher: Springer Science & Business Media
ISBN: 1441995692
Category : Mathematics
Languages : en
Pages : 409
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Book Description
"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.
Author: Robert Peter O'Donnell
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 210
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Book Description
The report presents a class of new algorithms for the approximate determination of the fixed points of 'operators' in normed linear spaces. The method of averaging functional corrections is itself a generalization of the classical method of successive approximations. Theoretical results concerning the convergence characteristics of the new algorithms are presented. The new methods are shown to be superior to the method of averaging functional corrections for certain types of operators. The primary application is to boundary value problems in integral equation form, and the representation of boundary value problems in this form is discussed. Other potential practical applications are considered. Numerical examples are given which demonstrate that the new algorithms are computational methods of significant practical value. (Author).
Author: G.A. Watson
Publisher: Springer
ISBN: 3540381295
Category : Mathematics
Languages : en
Pages : 214
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Book Description
