Download or read online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get book now. This site is like a library, Use search box in the widget to get ebook that you want.

Solving Nonlinear Equations with Newton s Method

Solving Nonlinear Equations with Newton s Method Author C. T. Kelley
ISBN-10 0898718899
Release 2003
Pages 104
Download Link Click Here

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.



Optimization and Nonlinear Equations

Optimization and Nonlinear Equations Author L. T. Watson
ISBN-10 0444505997
Release 2001
Pages 371
Download Link Click Here

/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume. Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts. The most efficient methods for local optimization, both unconstrained and constrained, are still derived from the classical Newton approach. As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented. Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation. Algorithms for nonlinear equations can be roughly classified as locally convergent or globally convergent. The characterization is not perfect. Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.



Iterative Methods for Linear and Nonlinear Equations

Iterative Methods for Linear and Nonlinear Equations Author C. T. Kelley
ISBN-10 1611970946
Release 1995
Pages 166
Download Link Click Here

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.



Numerical Methods for Unconstrained Optimization and Nonlinear Equations

Numerical Methods for Unconstrained Optimization and Nonlinear Equations Author J. E. Dennis, Jr.
ISBN-10 1611971209
Release 1996-12-01
Pages 378
Download Link Click Here

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.



Numerical Analysis

Numerical Analysis Author Walter Gautschi
ISBN-10 9780817682590
Release 2011-12-07
Pages 588
Download Link Click Here

Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.



Iterative Solution of Nonlinear Equations in Several Variables

Iterative Solution of Nonlinear Equations in Several Variables Author J. M. Ortega
ISBN-10 9781483276724
Release 2014-05-10
Pages 592
Download Link Click Here

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.



Haar Wavelets

Haar Wavelets Author Ülo Lepik
ISBN-10 9783319042954
Release 2014-01-09
Pages 207
Download Link Click Here

This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.



Programming for Computations Python

Programming for Computations   Python Author Svein Linge
ISBN-10 9783319324289
Release 2016-07-25
Pages 232
Download Link Click Here

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.



Memoirs of the Scientific Sections of the Academy of the Socialist Republic of Romania

Memoirs of the Scientific Sections of the Academy of the Socialist Republic of Romania Author
ISBN-10 UCBK:C086539032
Release 2011
Pages
Download Link Click Here

Memoirs of the Scientific Sections of the Academy of the Socialist Republic of Romania has been writing in one form or another for most of life. You can find so many inspiration from Memoirs of the Scientific Sections of the Academy of the Socialist Republic of Romania also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Memoirs of the Scientific Sections of the Academy of the Socialist Republic of Romania book for free.



Iterative Methods for Optimization

Iterative Methods for Optimization Author C. T. Kelley
ISBN-10 161197092X
Release 1999
Pages 180
Download Link Click Here

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.



Programming for Computations MATLAB Octave

Programming for Computations   MATLAB Octave Author Svein Linge
ISBN-10 9783319324524
Release 2016-08-01
Pages 216
Download Link Click Here

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.



Fundamentals of Structural Mechanics

Fundamentals of Structural Mechanics Author Keith D. Hjelmstad
ISBN-10 9780387233314
Release 2007-03-14
Pages 480
Download Link Click Here

A solid introduction to basic continuum mechanics, emphasizing variational formulations and numeric computation. The book offers a complete discussion of numerical method techniques used in the study of structural mechanics.



Computational Methods in Nonlinear Analysis

Computational Methods in Nonlinear Analysis Author Ioannis K Argyros
ISBN-10 9789814405843
Release 2013-07-11
Pages 592
Download Link Click Here

The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory. This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis. Contents:Newton's MethodsSpecial Conditions for Newton's MethodNewton's Method on Special SpacesSecant MethodGauss–Newton MethodHalley's MethodChebyshev's MethodBroyden's MethodNewton-like MethodsNewton–Tikhonov Method for Ill-posed Problems Readership: Graduate students and researchers in computational mathematics and nonlinear analysis. Keywords:Numerical Analysis;Nonlinear Equations;Nonlinear Analysis;Variational Inequalities;Fixed Point TheoryKey Features:The book contains recent results in the field of computational sciencesThe book updates the results of the 3 competing books: (1) Convergence and Applications of Newton-type iterations, springer–Verlag Publ., 2008 (author: Ioannis K Argyros) (2) Functional Analysis, Pergamon Press, Oxford, 1982 (authors: L V Kantorovich, G P Akilov) (3) Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970 (authors: L M Ortega, W C Rheinboldt)The book presents several applications and examples in engineering, mathematical physics, optimization and many other areasReviews: “This book is known as a reference book for advanced computational methods in nonlinear analysis.” Zentralblatt MATH “The material included in the monograph is new and mainly due to its authors. It synthesises the deep and long-standing research activity in the field. This book is mainly intended for researchers working in the area of theoretical computational methods but it could also be an important documentation source for practitioners in applied computational mathematics.” Mathematical Reviews Clippings



Advanced Computational Methods for Knowledge Engineering

Advanced Computational Methods for Knowledge Engineering Author Tien Van Do
ISBN-10 9783319065694
Release 2014-04-11
Pages 428
Download Link Click Here

The proceedings consists of 30 papers which have been selected and invited from the submissions to the 2nd International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA 2014) held on 8-9 May, 2014 in Budapest, Hungary. The conference is organized into 7 sessions: Advanced Optimization Methods and Their Applications, Queueing Models and Performance Evaluation, Software Development and Testing, Computational Methods for Mobile and Wireless Networks, Computational Methods for Knowledge Engineering, Logic Based Methods for Decision Making and Data Mining and Nonlinear Systems and Applications, respectively. All chapters in the book discuss theoretical and practical issues connected with computational methods and optimization methods for knowledge engineering. The editors hope that this volume can be useful for graduate and Ph.D. students and researchers in Computer Science and Applied Mathematics. It is the hope of the editors that readers of this volume can find many inspiring ideas and use them to their research. Many such challenges are suggested by particular approaches and models presented in individual chapters of this book.



Advances in Iterative Methods for Nonlinear Equations

Advances in Iterative Methods for Nonlinear Equations Author Sergio Amat
ISBN-10 9783319392288
Release 2016-10-29
Pages 286
Download Link Click Here

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.



Scientific Computing An Introduction using Maple and MATLAB

Scientific Computing   An Introduction using Maple and MATLAB Author Walter Gander
ISBN-10 9783319043258
Release 2014-04-23
Pages 905
Download Link Click Here

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.



Reliability in Computing

Reliability in Computing Author Ramon E. Moore
ISBN-10 9781483277844
Release 2014-05-10
Pages 444
Download Link Click Here

Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms. The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence. The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions. The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.