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  • 1
    Electronic Resource
    Electronic Resource
    On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms (1990)
    Springer
    Annals of the Institute of Statistical Mathematics 42 (1990), S. 387-401 
    Details
    ISSN: 1572-9052
    Keywords: Convergence theorems ; Broyden-like methods ; nonlinear equations ; nondifferentiable terms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the author studies a Broyden-like method for solving nonlinear equations with nondifferentiable terms, which uses as updating matrices, approximations for Jacobian matrices of differentiable terms. Local and semilocal convergence theorems are proved. The results generalize those of Broyden, Dennis and Moré.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00050844
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Convergence of Newton-like methods for singular operator equations using outer inverses (1993)
    Springer
    Numerische Mathematik 66 (1993), S. 235-257 
    Details
    ISSN: 0945-3245
    Keywords: 65J15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a (semilocal) Kantorovich-type analysis for Newton-like methods for singular operator equations using outer inverses. We establish sharp generalizations of the Kantorovich theory and the Mysovskii theory for operator equations when the derivative is not necessarily invertible. The results reduce in the case of an invertible derivative to well-known theorems of Kantorovich and Mysovskii with no additional assumptions, unlike earlier theorems which impose strong conditions. The strategy of the analysis is based on Banach-type lemmas and perturbation bounds for outer inverses which show that the set of outer inverses (to a given bounded linear operator) admits selections that behave like bounded linear inverses, in contrast to inner inverses or generalized inverses which do not depend continuously on perturbations of the operator. We give two examples to illustrate our results and compare them with earlier results, and another numerical example to relate our results to computational issues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385696
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Further developments towards a new virtual-pulse time integral methodology for general non-linear transient thermal analysis (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 961-970 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New developments of describing the theoretical basis towards an effective virtual-pulse (VIP) time integral methodology are proposed for general non-linear transient heat transfer problems. Primarily to validate the proposed methodology of computation, simple numerical test cases are provided and comparisons are also drawn with the implicit second-order-accurate Crank-Nicolson method. For the models tested, the proposed method has comparable or improved accuracy and stability characteristics. The VIP methodology introduced here for tackling non-linear thermal problems offers attractive features and is a viable alternative to traditional time-stepping practices. Efforts are underway to demonstrate the practical applicability to multi-dimensional thermal analysis.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640101202
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    Paper (German National Licenses)
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