Iterative Solution Of Nonlinear Systems Of Equations

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Iterative Methods for Solving Nonlinear Equations and Systems

Author : Juan R. Torregrosa
Publisher : MDPI
ISBN 13 : 3039219405
Total Pages : 494 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Iterative Methods for Solving Nonlinear Equations and Systems by : Juan R. Torregrosa

Download or read book Iterative Methods for Solving Nonlinear Equations and Systems written by Juan R. Torregrosa and published by MDPI. This book was released on 2019-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Solution of Nonlinear Equations in Several Variables

Author : J. M. Ortega
Publisher : Elsevier
ISBN 13 : 1483276724
Total Pages : 593 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Iterative Solution of Nonlinear Equations in Several Variables by : J. M. Ortega

Download or read book Iterative Solution of Nonlinear Equations in Several Variables written by J. M. Ortega and published by Elsevier. This book was released on 2014-05-10 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Iterative Methods for Linear and Nonlinear Equations

Author : C. T. Kelley
Publisher : SIAM
ISBN 13 : 9781611970944
Total Pages : 179 pages
Book Rating : 4.9/5 (79 download)

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Book Synopsis Iterative Methods for Linear and Nonlinear Equations by : C. T. Kelley

Download or read book Iterative Methods for Linear and Nonlinear Equations written by C. T. Kelley and published by SIAM. This book was released on 1995-01-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Sparse Linear Systems

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Methods for Solving Systems of Nonlinear Equations

Author : Werner C. Rheinboldt
Publisher : SIAM
ISBN 13 : 9781611970012
Total Pages : 157 pages
Book Rating : 4.9/5 (7 download)

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Book Synopsis Methods for Solving Systems of Nonlinear Equations by : Werner C. Rheinboldt

Download or read book Methods for Solving Systems of Nonlinear Equations written by Werner C. Rheinboldt and published by SIAM. This book was released on 1998-01-01 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Solving Nonlinear Equations with Newton's Method

Author : C. T. Kelley
Publisher : SIAM
ISBN 13 : 9780898718898
Total Pages : 117 pages
Book Rating : 4.7/5 (188 download)

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Book Synopsis Solving Nonlinear Equations with Newton's Method by : C. T. Kelley

Download or read book Solving Nonlinear Equations with Newton's Method written by C. T. Kelley and published by SIAM. This book was released on 2003-01-01 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Solution of Nonlinear Systems of Equations

Author : R. Ansorge
Publisher : Springer
ISBN 13 : 354039379X
Total Pages : 213 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Iterative Solution of Nonlinear Systems of Equations by : R. Ansorge

Download or read book Iterative Solution of Nonlinear Systems of Equations written by R. Ansorge and published by Springer. This book was released on 2006-11-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: a

Iterative Methods for Linear Systems

Author : Maxim A. Olshanskii
Publisher : SIAM
ISBN 13 : 1611973465
Total Pages : 257 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Iterative Methods for Linear Systems by : Maxim A. Olshanskii

Download or read book Iterative Methods for Linear Systems written by Maxim A. Olshanskii and published by SIAM. This book was released on 2014-07-21 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.??

Iterative Solution of Large Sparse Systems of Equations

Author : Wolfgang Hackbusch
Publisher : Springer
ISBN 13 : 0387940642
Total Pages : 460 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Iterative Solution of Large Sparse Systems of Equations by : Wolfgang Hackbusch

Download or read book Iterative Solution of Large Sparse Systems of Equations written by Wolfgang Hackbusch and published by Springer. This book was released on 1993-12-13 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c~ empfe~le 3~nen biegen IDlobu9 aur 9tac~a~mung. ec~werlic~ werben eie ie wieber bi reet eliminiren, wenigftens nic~t, wenn eie me~r als 2 Unbefannte ~aben. :Da9 inbirecte 93erfa~ren 109st sic~ ~alb im ec~lafe ausfii~ren, ober man fann wo~renb be9gelben an anbere :Dinge benfen. [CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e. , they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.

Programming for Computations - MATLAB/Octave

Author : Svein Linge
Publisher : Springer
ISBN 13 : 3319324527
Total Pages : 228 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Programming for Computations - MATLAB/Octave by : Svein Linge

Download or read book Programming for Computations - MATLAB/Octave written by Svein Linge and published by Springer. This book was released on 2016-08-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Iterative Methods for Solving Linear Systems

Author : Anne Greenbaum
Publisher : SIAM
ISBN 13 : 089871396X
Total Pages : 225 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Iterative Methods for Solving Linear Systems by : Anne Greenbaum

Download or read book Iterative Methods for Solving Linear Systems written by Anne Greenbaum and published by SIAM. This book was released on 1997-01-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Finite Difference Computing with PDEs

Author : Hans Petter Langtangen
Publisher : Springer
ISBN 13 : 3319554565
Total Pages : 522 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Finite Difference Computing with PDEs by : Hans Petter Langtangen

Download or read book Finite Difference Computing with PDEs written by Hans Petter Langtangen and published by Springer. This book was released on 2017-06-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Iterative Methods for the Solution of Equations

Author : Joseph Frederick Traub
Publisher : American Mathematical Soc.
ISBN 13 : 9780828403122
Total Pages : 328 pages
Book Rating : 4.4/5 (31 download)

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Book Synopsis Iterative Methods for the Solution of Equations by : Joseph Frederick Traub

Download or read book Iterative Methods for the Solution of Equations written by Joseph Frederick Traub and published by American Mathematical Soc.. This book was released on 1982 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ... ''

Advances in Iterative Methods for Nonlinear Equations

Author : Sergio Amat
Publisher : Springer
ISBN 13 : 331939228X
Total Pages : 286 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Advances in Iterative Methods for Nonlinear Equations by : Sergio Amat

Download or read book Advances in Iterative Methods for Nonlinear Equations written by Sergio Amat and published by Springer. This book was released on 2016-09-27 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Defect Correction Methods

Author : K. Böhmer
Publisher : Springer Science & Business Media
ISBN 13 : 3709170230
Total Pages : 247 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Defect Correction Methods by : K. Böhmer

Download or read book Defect Correction Methods written by K. Böhmer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years ago, the term "defect correction" was introduced to characterize a class of methods for the improvement of an approximate solution of an operator equation. This class includes many well-known techniques (e.g. Newton's method) but also some novel approaches which have turned out to be quite efficient. Meanwhile a large number of papers and reports, scattered over many journals and institutions, have appeared in this area. Therefore, a working conference on "Error Asymptotics and Defect Corrections" was organized by K. Bohmer, V. Pereyra and H. J. Stetter at the Mathematisches Forschungsinstitut Oberwolfach in July 1983, a meeting which aimed at bringing together a good number of the scientists who are active in this field. Altogether 26 persons attended, whose interests covered a wide spectrum from theoretical analyses to applications where defect corrections may be utilized; a list of the participants may be found in the Appendix. Most of the colleagues who presented formal lectures at the meeting agreed to publish their reports in this volume. It would be presumptuous to call this book a state-of-the-art report in defect corrections. It is rather a collection of snapshots of activities which have been going on in a number of segments on the frontiers of this area. No systematic coverage has been attempted. Some articles focus strongly on the basic concepts of defect correction; but in the majority of the contributions the defect correction ideas appear rather as instruments for the attainment of some specified goal.

Multipoint Methods for Solving Nonlinear Equations

Author : Miodrag Petkovic
Publisher : Academic Press
ISBN 13 : 0123972981
Total Pages : 317 pages
Book Rating : 4.1/5 (239 download)

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Book Synopsis Multipoint Methods for Solving Nonlinear Equations by : Miodrag Petkovic

Download or read book Multipoint Methods for Solving Nonlinear Equations written by Miodrag Petkovic and published by Academic Press. This book was released on 2012-12-31 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. - Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems - Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation - Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiency - Provides a powerful means of learning by systematic experimentation with some of the many fascinating problems in science - Includes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple

Algorithms for Continuous Optimization

Author : E. Spedicato
Publisher : Springer Science & Business Media
ISBN 13 : 9400903693
Total Pages : 572 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Algorithms for Continuous Optimization by : E. Spedicato

Download or read book Algorithms for Continuous Optimization written by E. Spedicato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute on "Algorithms for continuous optimiza tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.