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Zufiria Zatarain, Pedro José and Guttalu, Ramesh S. (1990). A computational method for finding all the roots of a vector function. "Applied Mathematics and Computation", v. 35 (n. 1); pp. 13-59. ISSN 0096-3003.
Title: | A computational method for finding all the roots of a vector function |
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Author/s: |
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Item Type: | Article |
Título de Revista/Publicación: | Applied Mathematics and Computation |
Date: | 1990 |
ISSN: | 0096-3003 |
Volume: | 35 |
Subjects: | |
Faculty: | E.T.S.I. Telecomunicación (UPM) |
Department: | Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones |
Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
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Based on dynamical systems theory, a computational method is proposed to locate all the roots of a nonlinear vector function. The computational approach utilizes the cell-mapping method. This method relies on discretization of the state space and is a convenient and powerful numerical tool for analyzing the global behavior of nonlinear systems. Our study shows that it is efficient and effective for determining roots because it minimizes and simplifies computations of system trajectories. Since the roots are asymptotically stable equilibrium points of the autonomous dynamical system, it also provides the domains of attraction associated with each root. Other numerical techniques based on iterative and homotopic methods can make use of these domains to choose appropriate initial guesses. Singular manifolds play an important role in limiting the extent of these domains of attraction. Both a theoretical basis and a computational algorithm for locating the singular manifolds are also provided. They make use of similar state-space discretization frameworks. Examples are given to illustrate the computational approaches. It is demonstrated that for one of the examples (a mechanical system), the method yields many more solutions than those previously reported.
Item ID: | 53498 |
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DC Identifier: | https://oa.upm.es/53498/ |
OAI Identifier: | oai:oa.upm.es:53498 |
Official URL: | https://www.sciencedirect.com/science/article/abs/... |
Deposited by: | Memoria Investigacion |
Deposited on: | 25 Mar 2019 18:47 |
Last Modified: | 25 Jan 2023 16:36 |