Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems
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Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems
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Author : Alexander Morgan
language : en
Publisher: SIAM
Release Date : 2009-06-04
Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems written by Alexander Morgan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-04 with Computers categories.
An elementary introduction to polynomial continuation.
Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems
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Author : Alexander Morgan
language : en
Publisher: Prentice Hall
Release Date : 1987
Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems written by Alexander Morgan and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science
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Author : Andrew John Sommese
language : en
Publisher: World Scientific
Release Date : 2005
The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science written by Andrew John Sommese and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.
Numerical Continuation Methods
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Author : Eugene L. Allgower
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Continuation Methods written by Eugene L. Allgower and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
Recipes For Continuation
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Author : Harry Dankowicz
language : en
Publisher: SIAM
Release Date : 2013-01-01
Recipes For Continuation written by Harry Dankowicz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Science categories.
This book provides a comprehensive introduction to the mathematical methodology of parameter continuation, the computational analysis of families of solutions to nonlinear mathematical equations. It develops a systematic formalism for constructing abstract representations of continuation problems and for implementing these in an existing computational platform. Recipes for Continuation lends equal importance to theoretical rigor, algorithm development, and software engineering; demonstrates the use of fully developed toolbox templates for single- and multisegment boundary-value problems to the analysis of periodic orbits in smooth and hybrid dynamical systems, quasi-periodic invariant tori, and homoclinic and heteroclinic connecting orbits between equilibria and/or periodic orbits; shows the use of vectorization for optimal computational efficiency, an object-oriented paradigm for the modular construction of continuation problems, and adaptive discretization algorithms for guaranteed bounds on estimated errors; and contains extensive and fully worked examples that illustrate the application of the MATLAB®-based Computational Continuation Core (COCO) to problems from recent research literature that are relevant to dynamical system models from mechanics, electronics, biology, economics, and neuroscience.
A Survey Of Lie Groups And Lie Algebras With Applications And Computational Methods
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Author : Johan G. F. Belinfante
language : en
Publisher: SIAM
Release Date : 1989-01-01
A Survey Of Lie Groups And Lie Algebras With Applications And Computational Methods written by Johan G. F. Belinfante and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
In this reprint edition, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed
21st Century Kinematics
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Author : J. Michael McCarthy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-04
21st Century Kinematics written by J. Michael McCarthy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-04 with Technology & Engineering categories.
21st Century Kinematics focuses on algebraic problems in the analysis and synthesis of mechanisms and robots, compliant mechanisms, cable-driven systems and protein kinematics. The specialist contributors provide the background for a series of presentations at the 2012 NSF Workshop. The text shows how the analysis and design of innovative mechanical systems yield increasingly complex systems of polynomials, characteristic of those systems. In doing so, it takes advantage of increasingly sophisticated computational tools developed for numerical algebraic geometry and demonstrates the now routine derivation of polynomial systems dwarfing the landmark problems of even the recent past. The 21st Century Kinematics workshop echoes the NSF-supported 1963 Yale Mechanisms Teachers Conference that taught a generation of university educators the fundamental principles of kinematic theory. As such these proceedings will provide admirable supporting theory for a graduate course in modern kinematics and should be of considerable interest to researchers in mechanical design, robotics or protein kinematics or who have a broader interest in algebraic geometry and its applications.
Multigrid Techniques
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Author : Achi Brandt
language : en
Publisher: SIAM
Release Date : 2011-07-07
Multigrid Techniques written by Achi Brandt and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-07 with Mathematics categories.
This revised edition of a classic text presents the best practices of developing multigrid solvers for large-scale computational problems. This book will be useful to practitioners and researchers, as well as students and instructors, in many areas of computational science and engineering, applied mathematics and numerical analysis.
Mathematical Models And Their Analysis
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Author : Frederick Y. M. Wan
language : en
Publisher: SIAM
Release Date : 2018-03-20
Mathematical Models And Their Analysis written by Frederick Y. M. Wan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-20 with Computers categories.
A great deal can be learned through modeling and mathematical analysis about real-life phenomena, even before numerical simulations are used to accurately portray the specific configuration of a situation. Scientific computing also becomes more effective and efficient if it is preceded by some preliminary analysis. These important advantages of mathematical modeling are demonstrated by models of historical importance in an easily understandable way. The organization of Mathematical Models and Their Analysis groups models by the issues that need to be addressed about the phenomena. The new approach shows how mathematics effective for one modeled phenomenon can be used to analyze another unrelated problem. For instance, the mathematics of differential equations useful in understanding the classical physics of planetary models, fluid motion, and heat conduction is also applicable to the seemingly unrelated phenomena of traffic flow and congestion, offshore sovereignty, and regulation of overfishing and deforestation. The formulation and in-depth analysis of these and other models on modern social issues, such as the management of exhaustible and renewable resources in response to consumption demands and economic growth, are of increasing concern to students and researchers of our time. The modeling of current social issues typically starts with a simple but meaningful model that may not capture all the important elements of the phenomenon. Predictions extracted from such a model may be informative but not compatible with all known observations; so the model may require improvements. The cycle of model formulation, analysis, interpretation, and assessment is made explicit for the modeler to repeat until a model is validated by consistency with all known facts.
The Method Of Weighted Residuals And Variational Principles
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Author : Bruce A. Finlayson
language : en
Publisher: SIAM
Release Date : 2013-12-30
The Method Of Weighted Residuals And Variational Principles written by Bruce A. Finlayson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-30 with Mathematics categories.
This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.