A computational method for finding all the roots of a vector function

Zufiria Zatarain, Pedro Jose 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.

Description

Title: A computational method for finding all the roots of a vector function
Author/s:
  • Zufiria Zatarain, Pedro Jose
  • Guttalu, Ramesh S.
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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Abstract

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.

More information

Item ID: 53498
DC Identifier: http://oa.upm.es/53498/
OAI Identifier: oai:oa.upm.es:53498
Official URL: https://www.sciencedirect.com/science/article/abs/pii/009630039090090P
Deposited by: Memoria Investigacion
Deposited on: 25 Mar 2019 18:47
Last Modified: 25 Mar 2019 18:47
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