Iterative Methods For Linear And Nonlinear Equations

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Iterative Methods for Linear and Nonlinear Equations

C. T. Kelley
Iterative Methods for Linear and Nonlinear Equations Book PDF

Author : C. T. Kelley
Publisher : SIAM
Page : 179 pages
File Size : 48,7 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 1611970946

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

Iterative Methods for Linear and Nonlinear Equations

C. T. Kelley
Iterative Methods for Linear and Nonlinear Equations Book PDF

Author : C. T. Kelley
Publisher : SIAM
Page : 169 pages
File Size : 43,7 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780898713527

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

Mathematics of Computing -- Numerical Analysis.

Iterative Methods for Solving Nonlinear Equations and Systems

Juan R. Torregrosa,Alicia Cordero,Fazlollah Soleymani
Iterative Methods for Solving Nonlinear Equations and Systems Book PDF

Author : Juan R. Torregrosa,Alicia Cordero,Fazlollah Soleymani
Publisher : MDPI
Page : 494 pages
File Size : 52,6 Mb
Release : 2019-12-06
Category : Mathematics
ISBN : 9783039219407

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Iterative Methods for Solving Nonlinear Equations and Systems by Juan R. Torregrosa,Alicia Cordero,Fazlollah Soleymani Pdf

Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Iterative Methods for Sparse Linear Systems

Yousef Saad
Iterative Methods for Sparse Linear Systems Book PDF

Author : Yousef Saad
Publisher : SIAM
Page : 537 pages
File Size : 41,9 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Mathematics of Computing -- General.

Iterative Methods for Solving Linear Systems

Anne Greenbaum
Iterative Methods for Solving Linear Systems Book PDF

Author : Anne Greenbaum
Publisher : SIAM
Page : 225 pages
File Size : 49,7 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713961

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Iterative Methods for Solving Linear Systems by Anne Greenbaum Pdf

Mathematics of Computing -- Numerical Analysis.

Iterative Methods and Preconditioners for Systems of Linear Equations

Gabriele Ciaramella,Martin J. Gander
Iterative Methods and Preconditioners for Systems of Linear Equations Book PDF

Author : Gabriele Ciaramella,Martin J. Gander
Publisher : SIAM
Page : 285 pages
File Size : 49,5 Mb
Release : 2022-02-08
Category : Mathematics
ISBN : 9781611976908

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Iterative Methods and Preconditioners for Systems of Linear Equations by Gabriele Ciaramella,Martin J. Gander Pdf

Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.

Iterative Methods for Linear Systems

Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
Iterative Methods for Linear Systems Book PDF

Author : Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
Publisher : SIAM
Page : 257 pages
File Size : 41,5 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781611973464

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Iterative Methods for Linear Systems by Maxim A. Olshanskii,Eugene E. Tyrtyshnikov Pdf

Iterative Methods for Linear Systems?offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.??

Advances in Iterative Methods for Nonlinear Equations

Sergio Amat,Sonia Busquier
Advances in Iterative Methods for Nonlinear Equations Book PDF

Author : Sergio Amat,Sonia Busquier
Publisher : Springer
Page : 286 pages
File Size : 55,5 Mb
Release : 2016-09-27
Category : Mathematics
ISBN : 9783319392288

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Advances in Iterative Methods for Nonlinear Equations by Sergio Amat,Sonia Busquier Pdf

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.

Iterative Solution of Nonlinear Equations in Several Variables

J. M. Ortega,W. C. Rheinboldt
Iterative Solution of Nonlinear Equations in Several Variables Book PDF

Author : J. M. Ortega,W. C. Rheinboldt
Publisher : Elsevier
Page : 593 pages
File Size : 44,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483276724

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Iterative Solution of Nonlinear Equations in Several Variables by J. M. Ortega,W. C. Rheinboldt Pdf

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.

Solving Nonlinear Equations with Newton's Method

C. T. Kelley
Solving Nonlinear Equations with Newton s Method Book PDF

Author : C. T. Kelley
Publisher : SIAM
Page : 117 pages
File Size : 43,6 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718899

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Solving Nonlinear Equations with Newton's Method by C. T. Kelley Pdf

This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.

Iterative Methods for Sparse Linear Systems

Yousef Saad
Iterative Methods for Sparse Linear Systems Book PDF

Author : Yousef Saad
Publisher : SIAM
Page : 546 pages
File Size : 50,7 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718007

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.

Solving Nonlinear Equations with Iterative Methods

C. T. Kelley
Solving Nonlinear Equations with Iterative Methods Book PDF

Author : C. T. Kelley
Publisher : SIAM
Page : 201 pages
File Size : 47,8 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 9781611977271

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Solving Nonlinear Equations with Iterative Methods by C. T. Kelley Pdf

This user-oriented guide describes state-of-the-art methods for nonlinear equations and shows, via algorithms in pseudocode and Julia with several examples, how to choose an appropriate iterative method for a given problem and write an efficient solver or apply one written by others. A sequel to the author’s Solving Nonlinear Equations with Newton’s Methods (SIAM, 2003), this book contains new material on pseudo-transient continuation, mixed-precision solvers, and Anderson acceleration. It is supported by a Julia package and a suite of Jupyter notebooks and includes examples of nonlinear problems from many disciplines. This book is will be useful to researchers who solve nonlinear equations, students in numerical analysis, and the Julia community.

Iterative Methods for Optimization

C. T. Kelley
Iterative Methods for Optimization Book PDF

Author : C. T. Kelley
Publisher : SIAM
Page : 195 pages
File Size : 48,7 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 161197092X

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Iterative Methods for Optimization by C. T. Kelley Pdf

This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.

Convergence of Iterative Methods Applied to Large Overdetermined Linear and Nonlinear Systems of Equations Using Least Squares

Charles O. Stearns,Leroy Romney Alldredge
Convergence of Iterative Methods Applied to Large Overdetermined Linear and Nonlinear Systems of Equations Using Least Squares Book PDF

Author : Charles O. Stearns,Leroy Romney Alldredge
Publisher : Unknown
Page : 20 pages
File Size : 51,7 Mb
Release : 1970
Category : Chebyshev polynomials
ISBN : PSU:000072016992

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Convergence of Iterative Methods Applied to Large Overdetermined Linear and Nonlinear Systems of Equations Using Least Squares by Charles O. Stearns,Leroy Romney Alldredge Pdf

Solutions are obtained to large overdetermined systems of equations. Both nonlinear and linear systems are considered. The nonlinear system represents a dipole model of the earth's geomagnetic field, which is generated from spherical harmonic coefficients. This system of 64 unknowns and 1836 equations is solved by a maximum neighborhood method, which is an optimum interpolation between the well known Taylor's series and steepest descent methods. The original given values of the generated field are as large as 60,000 gamma, whereas a rms residual of 27.9 gamma is obtained with 173 iterations. The linear system of equations represents dipole changes required to account for the earth's secular change field which is generated from spherical harmonic coefficients. The dipole parameters computed from the nonlinear model are used as input parameters. The system contains 64 unknowns and 612 equations and is solved using a Chebyshev polynomial iterative method. These results are compared to results obtained by a direct solution of the normal equations of the system and results obtained by a pseudo-inverse method using a modified Gram-Schmidt factorization. Although the latter two methods give smaller rms values than the iterative method, the results of the iterative method are more reasonable in view of known properties of the results. The generated field has a rms value of 45 gamma per year. An rms residual of 2.5 gamma per year was obtained after 25,000 iterations.

Numerical Methods for Unconstrained Optimization and Nonlinear Equations

J. E. Dennis, Jr.,Robert B. Schnabel
Numerical Methods for Unconstrained Optimization and Nonlinear Equations Book PDF

Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 46,9 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209

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Numerical Methods for Unconstrained Optimization and Nonlinear Equations by J. E. Dennis, Jr.,Robert B. Schnabel Pdf

This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.