Computational Solution Of Nonlinear Systems Of Equations

Author : Eugene L. Allgower,Kurt Georg
Publisher : American Mathematical Soc.
Page : 788 pages
File Size : 51,8 Mb
Release : 1990-04-03
Category : Mathematics
ISBN : 0821896946

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Computational Solution of Nonlinear Systems of Equations by Eugene L. Allgower,Kurt Georg Pdf

Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Author : Eugene L. Allgower,Kurt Georg
Publisher : American Mathematical Soc.
Page : 762 pages
File Size : 53,7 Mb
Release : 1990
Category : Mathematics
ISBN : 0821811312

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Computational Solution of Nonlinear Systems of Equations by Eugene L. Allgower,Kurt Georg Pdf

Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Author : George D. Byrne,Charles A. Hall
Publisher : Unknown
Page : 442 pages
File Size : 40,6 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015009789275

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Numerical Solution of Systems of Nonlinear Algebraic Equations by George D. Byrne,Charles A. Hall Pdf

Author : Louis B. Rall
Publisher : Unknown
Page : 254 pages
File Size : 43,8 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015013836062

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Computational Solution of Nonlinear Operator Equations by Louis B. Rall Pdf

Author : R. Ansorge,T. Meis,W. Törnig
Publisher : Springer
Page : 213 pages
File Size : 51,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540393795

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Iterative Solution of Nonlinear Systems of Equations by R. Ansorge,T. Meis,W. Törnig Pdf

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Author : George D. Byrne,Charles A. Hall
Publisher : Elsevier
Page : 430 pages
File Size : 45,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269306

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Numerical Solution of Systems of Nonlinear Algebraic Equations by George D. Byrne,Charles A. Hall Pdf

Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July 10-14, 1972. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics. The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. These topics are followed by a survey of some computational techniques for the nonlinear least squares problem. The remaining chapters explore the problem of nonlinear functional minimization, the modification methods, and the computer-oriented algorithms for solving system. These chapters also examine the principles of contractor theory of solving equations. This book will prove useful to undergraduate and graduate students.

Author : Juan R. Torregrosa,Alicia Cordero,Fazlollah Soleymani
Publisher : MDPI
Page : 494 pages
File Size : 45,9 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.

Author : J. M. Ortega,W. C. Rheinboldt
Publisher : SIAM
Page : 598 pages
File Size : 54,9 Mb
Release : 1970-01-01
Category : Mathematics
ISBN : 0898719461

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

Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time.

Author : Victoriano Carmona,Jesús Cuevas-Maraver,Fernando Fernández-Sánchez,Elisabeth García- Medina
Publisher : Springer
Page : 424 pages
File Size : 41,6 Mb
Release : 2018-09-15
Category : Science
ISBN : 9783319667669

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Nonlinear Systems, Vol. 1 by Victoriano Carmona,Jesús Cuevas-Maraver,Fernando Fernández-Sánchez,Elisabeth García- Medina Pdf

This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

Author : Werner C. Rheinboldt
Publisher : SIAM
Page : 157 pages
File Size : 49,7 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 1611970016

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Methods for Solving Systems of Nonlinear Equations by Werner C. Rheinboldt Pdf

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 : Tse-kʻo Wang,Zeke Wang,Senlin Xu,Tangan Gao,Tang'an Gao,Tʻang-an Kao
Publisher : Unknown
Page : 243 pages
File Size : 40,9 Mb
Release : 1994
Category : Computational complexity
ISBN : 7030039440

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Algebraic Systems of Equations and Computational Complexity Theory by Tse-kʻo Wang,Zeke Wang,Senlin Xu,Tangan Gao,Tang'an Gao,Tʻang-an Kao Pdf

Significant progress has been made during the last fifteen years in the solution of nonlinear systems, particularly in computing fixed points, solving systems of nonlinear equations and applications to equilibrium models. This volume presents a self-contained account of recent work on simplicial and continuation methods applied to the solution of algebraic equations. The contents are divided into eight chapters. Chapters 1 and 2 deal with Kuhn's algorithm; Chapter 3 considers Newton's method, and a comparison between Kuhn's algorithm and Newton's method is presented in Chapter 4. The following four chapters discuss respectively, incremental algorithms and their cost theory, homotopy algorithms, zeros of polynomial mapping, and piecewise linear algorithms. For researchers and graduates interested in algebraic equations and computational complexity theory.

Author : Anonim
Publisher : Academic Press
Page : 322 pages
File Size : 54,7 Mb
Release : 1971-03-31
Category : Mathematics
ISBN : 0080955835

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Numerical Solution of Ordinary Differential Equations by Anonim Pdf

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Author : Krzysztof A. Sikorski
Publisher : Oxford University Press
Page : 256 pages
File Size : 45,9 Mb
Release : 2001-01-18
Category : Computers
ISBN : 0198026676

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Optimal Solution of Nonlinear Equations by Krzysztof A. Sikorski Pdf

Optimal Solution of Nonlinear Equations is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping, and for the computation of the topological degree. It is of interest to any reader working in the area of Information-Based Complexity. The worst-case settings are analyzed here. Several classes of functions are studied with special emphasis on tight complexity bounds and methods which are close to or achieve these bounds. Each chapter ends with exercises, including companies and open-ended research based exercises.

Author : Eugene L. Allgower,Kurt Georg
Publisher : SIAM
Page : 409 pages
File Size : 49,5 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9780898715446

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Introduction to Numerical Continuation Methods by Eugene L. Allgower,Kurt Georg Pdf

Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.

Author : Svein Linge,Hans Petter Langtangen
Publisher : Springer
Page : 228 pages
File Size : 40,5 Mb
Release : 2016-08-01
Category : Computers
ISBN : 9783319324524

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Programming for Computations - MATLAB/Octave by Svein Linge,Hans Petter Langtangen Pdf

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.