Download Convergence Of The Iteration Process In The Solution Of Algebraic And Transcendental Equations full books in PDF, epub, and Kindle. Read online free Convergence Of The Iteration Process In The Solution Of Algebraic And Transcendental Equations ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : James R. Anderson |
| Publisher | : |
| Total Pages | : 62 |
| Release | : 1970 |
| Genre | : Equations |
| ISBN | : |
| Author | : Stephen Thomas Kowel |
| Publisher | : |
| Total Pages | : 9 |
| Release | : 1964 |
| Genre | : Mathematics |
| ISBN | : |
A simple, general method of solving transcendental equations is presented. Quantitative relations concerning the rate of convergence of the process are developed, and several examples are worked.
| Author | : Joseph Frederick Traub |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 328 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : 9780828403122 |
From the Preface (1964): ``This book presents a general theory of iteration algorithms for the numerical solution of equations and systems of equations. The relationship between the quantity and the quality of information used by an algorithm and the efficiency of the algorithm is investigated. Iteration functions are divided into four classes depending on whether they use new information at one or at several points and whether or not they reuse old information. Known iteration functions are systematized and new classes of computationally effective iteration functions are introduced. Our interest in the efficient use of information is influenced by the widespread use of computing machines ... The mathematical foundations of our subject are treated with rigor, but rigor in itself is not the main object. Some of the material is of wider application ... Most of the material is new and unpublished. Every attempt has been made to keep the subject in proper historical perspective ... ''
| Author | : Owe Axelsson |
| Publisher | : Cambridge University Press |
| Total Pages | : 676 |
| Release | : 1996-03-29 |
| Genre | : Mathematics |
| ISBN | : 9780521555692 |
This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.
| Author | : Olavi Nevanlinna |
| Publisher | : Birkhäuser |
| Total Pages | : 187 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034885474 |
Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and focuses on the dynamical aspects of the iteration processes. For example, there are many similarities between the evolution of a Krylov subspace process and that of linear operator semigroups, in particular in the beginning of the iteration. A lifespan of an iteration might typically start with a fast but slowing phase. Such a behavior is sublinear in nature, and is essentially independent of whether the problem is singular or not. Then, for nonsingular problems, the iteration might run with a linear speed before a possible superlinear phase. All these phases are based on different mathematical mechanisms which the book outlines. The goal is to know how to precondition effectively, both in the case of "numerical linear algebra" (where one usually thinks of first fixing a finite dimensional problem to be solved) and in function spaces where the "preconditioning" corresponds to software which approximately solves the original problem.
| Author | : V. L. Zaguskin |
| Publisher | : Elsevier |
| Total Pages | : 216 |
| Release | : 2014-05-12 |
| Genre | : Mathematics |
| ISBN | : 1483225674 |
Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations provides information pertinent to algebraic and transcendental equations. This book indicates a well-grounded plan for the solution of an approximate equation. Organized into six chapters, this book begins with an overview of the solution of various equations. This text then outlines a non-traditional theory of the solution of approximate equations. Other chapters consider the approximate methods for the calculation of roots of algebraic equations. This book discusses as well the methods for making roots more accurate, which are essential in the practical application of Berstoi's method. The final chapter deals with the methods for the solution of simultaneous linear equations, which are divided into direct methods and methods of successive approximation. This book is a valuable resource for students, engineers, and research workers of institutes and industrial enterprises who are using mathematical methods in the solution of technical problems.
| Author | : Sergio Amat |
| Publisher | : Springer |
| Total Pages | : 286 |
| Release | : 2016-09-27 |
| Genre | : Mathematics |
| ISBN | : 331939228X |
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.
| Author | : Ioannis Konstantinos Argyros |
| Publisher | : CRC Press |
| Total Pages | : 366 |
| Release | : 2017-07-12 |
| Genre | : Mathematics |
| ISBN | : 1498763626 |
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.
| Author | : Santanu Saha Ray |
| Publisher | : CRC Press |
| Total Pages | : 708 |
| Release | : 2018-09-03 |
| Genre | : Mathematics |
| ISBN | : 131536221X |
Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.
| Author | : Vantsyan Anushavan |
| Publisher | : LAP Lambert Academic Publishing |
| Total Pages | : 60 |
| Release | : 2014-12-11 |
| Genre | : |
| ISBN | : 9783659643583 |
In the monograph a nonlinear method of iteration is suggested a hybrid of the classical method of iteration and the method of proportional division. Algebraic evidence and the geometrical interpretation of convergence of the offered nonlinear-generalized process of iteration are given. The formulas for nonlinear operators of scalar and vector contraction mapping as functions of one and several real variables are obtained.
