Aspects Of The Computational Theory For Certain Iterative Methods
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Aspects Of The Computational Theory For Certain Iterative Methods
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Author : Ioannis K. Argyros
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2009
Aspects Of The Computational Theory For Certain Iterative Methods written by Ioannis K. Argyros and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Aspects Of The Computational Theory For Certain Iterative Methods
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Author : Ioannis K. Argyros
language : en
Publisher:
Release Date : 2009
Aspects Of The Computational Theory For Certain Iterative Methods written by Ioannis K. Argyros and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Computational Theory Of Iterative Methods
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Author : Ioannis Argyros
language : en
Publisher: Elsevier
Release Date : 2007-09-04
Computational Theory Of Iterative Methods written by Ioannis Argyros and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-04 with Mathematics categories.
The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.- Latest convergence results for the iterative methods - Iterative methods with the least computational cost- Iterative methods with the weakest convergence conditions- Open problems on iterative methods
Numerical Methods For Equations And Its Applications
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Author : Ioannis K. Argyros
language : en
Publisher: CRC Press
Release Date : 2012-06-05
Numerical Methods For Equations And Its Applications written by Ioannis K. Argyros and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-05 with Mathematics categories.
This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter co
Elements Of The General Theory Of Optimal Algorithms
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Author : Ivan V. Sergienko
language : en
Publisher: Springer Nature
Release Date : 2022-01-11
Elements Of The General Theory Of Optimal Algorithms written by Ivan V. Sergienko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-11 with Mathematics categories.
In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.
Hilbert Space Splittings And Iterative Methods
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Author : Michael Griebel
language : en
Publisher: Springer Nature
Release Date : 2024-11-06
Hilbert Space Splittings And Iterative Methods written by Michael Griebel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.
This book is about the theory of so-called Schwarz methods for solving variational problems in a Hilbert space V arising from linear equations and their associated quadratic minimization problems. Schwarz methods are based on the construction of a sequence of approximate solutions by solving auxiliary variational problems on a set of (smaller, finite-dimensional) Hilbert spaces $V_i$ in a certain order, combining them, and using the combined approximations in an iterative procedure. The spaces $V_i$ form a so-called space splitting for V, they need not necessarily be subspaces of V, and their number can be finite or infinite. The convergence behavior of Schwarz methods is influenced by certain properties of the space splittings they are based on. These properties are identified, and a detailed treatment of traditional deterministic and more recent greedy and stochastic orderings in the subproblem solution process is given, together with an investigation of accelerated methods. To illustrate the abstract theory, the numerical linear algebra analogs of the iterative methods covered in the book are discussed. Its standard application to the convergence theory of multilevel and domain decomposition methods for solving PDE problems is explained, and links to optimization theory and online learning algorithms are given. Providing an introduction and overview of iterative methods which are based on problem decompositions and suitable for parallel and distributed computing, the book could serve as the basis for a one- or two-semester course for M.S. and Ph.D. students specializing in numerical analysis and scientific computing. It will also appeal to a wide range of researchers interested in scientific computing in the broadest sense.
Iterative Methods For Sparse Linear Systems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2003-04-01
Iterative Methods For Sparse Linear Systems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-01 with Mathematics categories.
Mathematics of Computing -- General.
Computational Methods For Inverse Problems
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Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01
Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Iterative Solution Of Nonlinear Equations In Several Variables
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Author : J. M. Ortega
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Iterative Solution Of Nonlinear Equations In Several Variables written by J. M. Ortega and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.
Applied Iterative Methods
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Author : Louis A. Hageman
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Applied Iterative Methods written by Louis A. Hageman and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Applied Iterative Methods