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13 edition of Convergence and Applications of Newton-type Iterations found in the catalog.

Convergence and Applications of Newton-type Iterations

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Published by Springer .
Written in English


The Physical Object
Number of Pages528
ID Numbers
Open LibraryOL7447894M
ISBN 100387727418
ISBN 109780387727417

A FIXED POINT PROOF OF THE CONVERGENCE OF A NEWTON-TYPE METHOD VASILE BERINDE∗ AND MAD˘ ALINA P˘ ACURAR˘ ∗∗ ∗Department of Mathematics and Computer Science North University of Baia Mare Victor Baia Mare, Romania E-mail: [email protected], vasile [email protected] ∗∗Department of Statistics, Forecast and Mathematics.


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Convergence and Applications of Newton-type Iterations by Ioannis K. Argyros Download PDF EPUB FB2

"The book is devoted to iterative methods of approximative solving nonlinear operator equations. The main part of the book deals with the classical Newton-Kantorovich method. Undoubtedly, it can be used for an advanced study of the Newton-Kantorovich method and other iterative methods of approximate solving nonlinear operator by: The book assumes a basic background in linear algebra and numerical functional analysis.

Graduate students and researchers will find this book useful. It may be used as a self-study reference or as a supplementary text for an advanced course in numerical functional analysis.

Get this from a library. Convergence and applications of Newton-type iterations. [Ioannis K Argyros] -- "Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods.

This monograph provides a comprehensive study. Find many great new & used options and get the best deals for Convergence and Applications of Newton-Type Iterations by Ioannis K.

Argyros (, Hardcover) at the best online prices at eBay. Free shipping for many products. Guidelines for Convergence Authors; MAA FOCUS; Math Horizons; Submissions to MAA Periodicals; Guide for Referees; MAA Press (an imprint of the AMS) MAA Notes; MAA Reviews. Browse; MAA Library Recommendations; Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Communication; Information for Libraries; Author Resources.

Newton-like methods with increasing order of convergence and their convergence analysis in Banach space convergence of a three steps Newton-type iterative process under mild convergence. for other algorithms. It has a theoretical purpose enabling rates of convergence to be determined easily by showing that the algorithm of interest behaves asymptotically similarly to Newton’s method.

Naturally a lot has been written about the method and a classic book well worth reading is that by Ortega and Rheinboldt [11]. OtherFile Size: KB. A faster King–Werner-type iteration and its convergence analysis.

The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a. Convergence and Applications of Newton-type Iterations.

Convergence and Applications of Newton-type Iterations pp | Cite asAuthor: Ioannis K. Argyros. The present paper deals with ninth and seventh order convergent Newton-type iterative methods for approximating the simple roots α of nonlinear equations f(x) = 0, that is, f(α) = 0 and f′(α) ≠ 0.

Ninth order convergent Newton-type iterative method is a three step method, which includes five evaluations of the function per iteration Cited by: Convergence and Applications of Newton-type Iterations by Ioannis K. Argyros $ This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis.

and the stability theorem of Uzawa. The book explores conditions for the. Convergence and Applications of Newton-type Iterations.

Ioannis K. Argyros. Published by Springer () ISBN Convergence and Applications of Newton-type Iterations. Argyros, Ioannis K. Published by Condition: NEW. This listing is a new book, a title currently in-print which we order directly and immediately from the. A general iterative process is proposed, from which a class of parallel Newton-type iterative methods can be derived.

A unified convergence theorem for the general iterative process is established. The convergence of these Newton-type iterative methods is obtained from the unified convergence theorem.

The results of efficiency analyses and numerical example are : Qinglong Huang. In this chapter, we present an overview of some multipoint iterative methods for solving nonlinear systems obtained by using different techniques such as composition of known methods, weight function procedure, and pseudo-composition, etc.

The dynamical study of these iterative schemes provides us valuable information about their stability and : Alicia Cordero, Juan R. Torregrosa, Maria P.

Vassileva. This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems.

A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. A General Convergence Analysis of Some Newton-Type Methods for Nonlinear Inverse Problems.

On the iteratively regularized Gauss–Newton method in Banach spaces with applications to parameter identification problems. Numerische On the order optimality of the regularization via inexact Newton iterations.

Numerische Mathematik Cited by: Convergence analysis of inexact proximal Newton-type methods Jason D. Lee and Yuekai Sun Institute for Computational and Mathematical Engineering Stanford University, Stanford, CA fjdl17,[email protected] Michael A.

Saunders Department of Management Science and Engrineering Stanford University, Stanford, CA [email protected] Abstract. The book is divided into three parts: operations research, dynamics, and applications.

The operations research section deals with the convergence of Newton-type iterations for solving nonlinear equations and optimum problems, the limiting properties of the Nash bargaining solution, the utilization of public goods, and optimizing lot sizes in. Author of Advances in the Efficiency of Computational Methods and Applications, Approximate Solution of Operator Equations with Applications, The theory and applications of iteration methods, Polynomial operator equations in abstract spaces and applications, Newton Methods, Numerical methods for equations and its applications, Convergence and applications of Newton-type iterations.

We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator.

Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus Cited by: 1. A new technique has been developed to extend the convergence domain of Newton’s method.

The novelty of it is that no additional criteria are needed than in earlier studies [7,8] for convergence in both the local as well as the semi-local convergence of Newton’s have given the sufficient convergence criteria of earlier studies and then demonstrated the superiority of our new : Cristina Amorós, Ioannis K.

Argyros, Daniel González, Ángel Alberto Magreñán, Samundra Regmi, Íñigo. i.e., and the convergence is quadratic. The difficulty is the multiplicity of a root is unknown ahead of time.

If is used blindly some root may be skipped, and the iteration may oscillate around the real root. Example: Consider solving which has a double root and a single the following, we compare the performance of both and.

First use an initial guess. IntroducEon% • Newton’s%Method%(also%known%as%Newton#Raphson%Method)% is%used%to%solve%nonlinear%(system)%of%equaons,%which%can%be% represented%as%follows:%File Size: KB.

In order to improve the convergence order of Newton-type methods, many higher order approaches have been proposed in past years. In particular, there is much literature focused on the nonlinear scalar function. Petković et al.

provide a survey, many of which are presented in the book (Petković et al. a).Cited by: 2. The Gauss–Newton method for solving nonlinear least squares problems is studied in this paper.

Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local convergence analysis is by: In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f ′, and an.

The main contribution of this article is an efficient algorithmic trick to generate the quantities needed for a Newton-type method on the augmented (“lifted”) system with (a) almost no additional computational cost per iteration compared to a nonlifted Newton method, and (b) with negligible programming by: point then the chance of convergence of the iterative process is high.

Remark: If g is invertible then l0 is a flxed point of g if and only if l0 is a flxed point of g¡1: In view of this fact, sometimes we can apply the flxed point iteration method for g¡1 instead of g. For understanding, consider File Size: 82KB. This book is dedicated to the approximation of solutions of nonlinear equations using iterative methods.

The study about convergence matter of iterative methods is usually based on two categories: semi-local and local convergence analysis. Recently, there has been some progress on Newton-type methods with cubic convergence that do not require the computation of second derivatives.

Weerakoon and Fernando (Appl. Math. Lett. 13 () 87) derived the Newton method and a cubically convergent variant by rectangular and trapezoidal approximations to Newton’s theorem. respectively. Then a nested Newton-type algorithm of RE is derived by linearizing, in order, 1 () and 2 () in the inner and in the outer cycle, respectively.

For wide class of constitutive relationships and all flow regimes, convergence of the iterations is ensured for any time step size. Details of. Convergence and Applications of Newton-type Iterations Ioannis K.

Argyros Convergence and Applications of Newton-type Iterations Ioannis K. Argyros Department of Mathematical Sciences Cameron University Lawton, OK USA [email protected] ISBN: e-ISBN: DOI: / Library of Congress Control Number:.

Free Boundary Problems book. Theory and Applications. Free Boundary Problems. DOI link for Free Boundary Problems. Free Boundary Problems book. Theory and Applications. By Ioannis Athanasopoulos. Edition 1st Edition. First Published iterations, which is essentially less than 6.

More details about the convergence analysis of Newton’s method can be found in Boyed’s book on page As amazing as its quick convergence, it is important to keep in mind that the convergence result is in terms of number of iterations. [Fast Download] Convergence and Applications of Newton-type Iterations Related eBooks: Linear Algebra with Applications, Second Edition Applied Proof Theory Nexus Network Jour1 Advances in Brain Inspired Cognitive Systems How Much Inequality Is Fair?.

In the survey of the continuous nonlinear resource allocation problem, Patriksson pointed out that Newton-type algorithms have not been proposed for solving the problem of search theory in the theoretical perspective.

In this paper, we propose a Newton-type algorithm to solve the problem. We prove that the proposed algorithm has global and superlinear by: 3. In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent.

Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than. We give some sufficient semilocal conditions relating \(\varphi\) and \(P\) for these iterations to converge to a solution with a given convergence order.

As particular instances, we obtain convergence results for the Newton, Chebyshev and Steffensen mehods. Let P, X and Y be Banach spaces. Suppose that f: P × X → Y is continuously Frechet differentiable function depend on the point (p, x) and F: X ⇒ 2^Y is a set-valued mapping with closed graph.

Consider the following parametric generalized equation of the form: 0 ∈ f(p, x) + F(x). (1) In the present paper, we study an extended Newton-type method for solving parametric generalized Author: Mohammed Harunor Rashid.

excellent text book \Numerical Optimization" by Jorge Nocedal and Steve Wright [4]. This book 8 Local Convergence of General Newton Type Iterations 58 Optimization algorithms are used in many applications from diverse areas. Business: Allocation of resources in logistics, investment, etc.

File Size: 1MB. Kmc Km - $ Kmc Km Newton Center Cap ksb New Fits All Size Satin Black Wheels.On an Aitken-Steffensen-Newton type method 11 Oct Abstract We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations.In the last two decades, the field of inverse problems has certainly been one of the fastest growing areas in applied mathematics.

This growth has largely been driven by the needs of applications both in other sciences and in industry. In Chapter 1, we will give a short overview over some classes of inverse problems of practical interest.

Like everything in this book, this overview is far from.