Analysis And Computation Of Fixed Points
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Analysis And Computation Of Fixed Points
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Author : Stephen M. Robinson
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Analysis And Computation Of Fixed Points written by Stephen M. Robinson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.
Analysis And Computation Of Fixed Points
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Author : Stephen M. Robinson
language : en
Publisher:
Release Date : 1980
Analysis And Computation Of Fixed Points written by Stephen M. Robinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Analysis And Computation Of Fixed Points
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Author :
language : en
Publisher:
Release Date : 1980
Analysis And Computation Of Fixed Points written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Fixed Points
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Author : Stepan Karamardian
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Fixed Points written by Stepan Karamardian and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann’s iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.
Analysis And Computation Of Fixed Points
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Author : Stephen M. Robinson
language : en
Publisher:
Release Date : 1980
Analysis And Computation Of Fixed Points written by Stephen M. Robinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
The Computation Of Fixed Points And Applications
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Author : M. J. Todd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Computation Of Fixed Points And Applications written by M. J. Todd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore via triangu- tions. For this reason, Scarf is cited less in this manuscript than his contri- tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans [28] apply fixed-point methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf [56,58], Shapley [59], and Garcia, Lemke and Luethi [24]. Allgower [1] and Jeppson [31] use fixed-point algorithms to find many solutions to boundary-value problems.
Local Computation Of Simultaneous Fixed Points
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Author : Aarhus Universitet. Regionale EDB-center
language : en
Publisher:
Release Date : 1992
Local Computation Of Simultaneous Fixed Points written by Aarhus Universitet. Regionale EDB-center and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computer algorithms categories.
We will illustrate this point by tailoring the general algorithm to concrete examples in such (apparently) diverse areas as type inference, model checking, and strictness analysis. Especially in connection with the last example, strictness analysis, and more generally abstract interpretation, it is illustrated how the local algorithm provides a very minimal approach when determining the fixed-points, reminiscent of, but improving upon, what is known as Pending Analysis [19]. In the case of model checking a specialised version of the algorithm has already improved on earlier known local algorithms [2, 1]."
Fixed Point Theory And Applications
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Author : Kok Keong Tan
language : en
Publisher:
Release Date : 1992
Fixed Point Theory And Applications written by Kok Keong Tan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Fixed point theory categories.
Computational Methods In Nonlinear Analysis
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Author : Ioannis K. Argyros
language : en
Publisher: World Scientific
Release Date : 2013
Computational Methods In Nonlinear Analysis written by Ioannis K. Argyros and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory. This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.
Totally Convex Functions For Fixed Points Computation And Infinite Dimensional Optimization
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Author : Dan Butnariu
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Totally Convex Functions For Fixed Points Computation And Infinite Dimensional Optimization written by Dan Butnariu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, total convexity, is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making a general approach possible the work aims to improve upon classical results like the Holder-Minkowsky inequality of ℒp.