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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 1 (1990), S. 143-191 
    ISSN: 1573-269X
    Keywords: Nonlinear systems ; homotopy algorithm ; globally convergent ; probability-one homotopy ; path tracking ; continuation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Probability-one homotopy methods are a class of algorithms for solving nonlinear systems of equations that are accurate, robust, and converge from an arbitrary starting point almost surely. These new globally convergent homotopy techniques have been successfully applied to solve Brouwer fixed point problems, polynomial systems of equations, constrained and unconstrained optimization problems, discretizations of nonlinear two-point boundary value problems based on shooting, finite differences, collocation, and finite elements, and finite difference, collocation, and Galerkin approximations to nonlinear partial differential equations. This paper introduces, in a tutorial fashion, the theory of globally convergent homotopy algorithms, deseribes some computer algorithms and mathematical software, and presents several nontrivial engineering applications.
    Type of Medium: Electronic Resource
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