Computational Theory of Iterative Methods Books

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Computational Theory of Iterative Methods


Computational Theory of Iterative Methods
  • Author : Ioannis Argyros
  • Publisher : Elsevier
  • Release : 2007-09-04
  • ISBN : 0080560709
  • Language : En, Es, Fr & De
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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

Aspects of the Computational Theory for Certain Iterative Methods


Aspects of the Computational Theory for Certain Iterative Methods
  • Author : Ioannis Konstantinos Argyros
  • Publisher : Polimetrica s.a.s.
  • Release : 2009
  • ISBN : 9788876991516
  • Language : En, Es, Fr & De
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A Contemporary Study of Iterative Methods


A Contemporary Study of Iterative Methods
  • Author : A. Alberto Magrenan
  • Publisher : Academic Press
  • Release : 2018-02-13
  • ISBN : 9780128094938
  • Language : En, Es, Fr & De
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A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand. Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography Explores the uses of computation of iterative methods across non-linear analysis Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options

Iterative Methods and Their Dynamics with Applications


Iterative Methods and Their Dynamics with Applications
  • Author : Ioannis Konstantinos Argyros
  • Publisher : CRC Press
  • Release : 2017-07-12
  • ISBN : 9781498763622
  • Language : En, Es, Fr & De
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Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis. The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences or Applied Sciences. Moreover, the newest techniques used to study the dynamics of iterative methods are described and used in the book and they are compared with the classical ones.

Functions of Matrices


Functions of Matrices
  • Author : Nicholas J. Higham
  • Publisher : SIAM
  • Release : 2008
  • ISBN : 9780898717778
  • Language : En, Es, Fr & De
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A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.