Iterative Methods for Linear and Nonlinear Equations PDF Download
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Author: C. T. Kelley
Publisher: SIAM
ISBN: 9781611970944
Category : Mathematics
Languages : en
Pages : 179
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Book Description
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.
Author: C. T. Kelley
Publisher: SIAM
ISBN: 9781611970944
Category : Mathematics
Languages : en
Pages : 179
Get Book Here
Book Description
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.
Author: C. T. Kelley
Publisher: SIAM
ISBN: 9780898718898
Category : Mathematics
Languages : en
Pages : 117
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Book Description
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.
Author: Werner C. Rheinboldt
Publisher: SIAM
ISBN: 9781611970012
Category : Mathematics
Languages : en
Pages : 157
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Book Description
This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.
Author: Juan R. Torregrosa
Publisher: MDPI
ISBN: 3039219405
Category : Mathematics
Languages : en
Pages : 494
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Book Description
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.
Author: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537
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Book Description
Mathematics of Computing -- General.
Author: Sergio Amat
Publisher: Springer
ISBN: 331939228X
Category : Mathematics
Languages : en
Pages : 286
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Book Description
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: Adomian
Publisher: Academic Press
ISBN: 0080956750
Category : Computers
Languages : en
Pages : 352
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Book Description
Stochastic Systems
Author: A. Alberto Magrenan
Publisher: Academic Press
ISBN: 0128094931
Category : Mathematics
Languages : en
Pages : 402
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Book Description
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
Author: J. E. Dennis, Jr.
Publisher: SIAM
ISBN: 0898713641
Category : Mathematics
Languages : en
Pages : 390
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Book Description
A complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations.
Author: Maxim A. Olshanskii
Publisher: SIAM
ISBN: 1611973465
Category : Mathematics
Languages : en
Pages : 257
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Book Description
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.??
