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  • Articles  (7)
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  • Articles  (7)
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  • Springer  (7)
  • American Institute of Physics
  • Institute of Physics
  • Oxford University Press
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  • 1995-1999
  • 1980-1984  (7)
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  • Mathematics  (7)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
  • 1
    Electronic Resource
    Electronic Resource
    Root finding by divided differences (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 93-104 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65H05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A recursive method is presented for computing a simple zero of an analytic functionf from information contained in a table of divided differences of its reciprocalh=1/f. A good deal of flexibility is permitted in the choice of ordinate and derivative values, and in the choice of the number of previous points upon which to base the next estimate of the required zero. The method is shown to be equivalent to a process of fitting rational functions with linear numerators to data sampled fromf. Asymptotic and regional convergence properties of such a process have already been studied; in particular, asymptotically quadratic convergence is easily obtained, at the expense of only one function evaluation and a moderate amount of “overhead” computation per step. In these respects the method is comparable with the Newton form of iterated polynomial inverse interpolation, while its regional convergence characteristics may be superior in certain circum-stances. It is also shown that the method is not unduly sensitive to round-off errors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396188
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  • 2
    Electronic Resource
    Electronic Resource
    Superlinear convergence of symmetric Huang's class of methods (1981)
    Springer
    Numerische Mathematik 38 (1981), S. 209-218 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper the problem of minimizing the functionalf:D∈R n →R is considered. Typical assumptions onf are assumed. A class of Quasi-Newton methods, namely Huang's class of methods is used for finding an optimal solution of this problem. A new theorem connected with this class is presented. By means of this theorem some convergence results known up till now only for the methods which satisfy Quasi-Newton condition are extended, that is the results of superlinear convergence of variable metric methods in the cases of exact and asymptotically exact minimization and the so-called direct-prediction case. This theorem allows to interpretate one of the parameters as the scaling parameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397090
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  • 3
    Electronic Resource
    Electronic Resource
    Quasi-Newton-Verfahren vom Rang-Eins-Typ zur Lösung unrestringierter Minimierungsprobleme (1981)
    Springer
    Numerische Mathematik 38 (1981), S. 219-228 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper new Quasi-Newton methods of rank-one type for solving the unconstrained minimization problem are developed. The methods belong to the Oren-Luenberger class (for negative parametersΘ k ) and they generate always positive definite updating matrices. Moreover it is shown that these methods are invariant by scaling of the objective function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397091
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  • 4
    Electronic Resource
    Electronic Resource
    Quasi-Newton-Verfahren vom Rang-Eins-Typ zur Lösung unrestringierter Minimierungsprobleme (1981)
    Springer
    Numerische Mathematik 38 (1981), S. 229-244 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that the methods developed in part I of this paper [6] converge at leastn-step quadratically to the global minimum point of the objective functionf, if the Hessian off is uniformly positive definite, uniformly bounded and Lipschitz continuous and if the method is used with restart and asymptotically exact line search.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397092
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  • 5
    Electronic Resource
    Electronic Resource
    Une méthode numérique pour le calcul des points de retournement. Application à un problème aux limites non-linéaire (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 433-444 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An iterative method is presented for determining a turning point in a branch of solutions of an algebraic system of equations depending on a parameter. One shows that the convergence is superlinear and that this method may constitute a complement for the Newton method. With a finite element method, numerical results are given testing the process on the discrete version of a mildly nonlinear boundary value problem to determine the turning point in the positive solution branch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400320
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  • 6
    Electronic Resource
    Electronic Resource
    Global approximate Newton methods (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 279-295 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H 10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We derive a class of globally and quadratically converging algorithms for a system of nonlinear equations,g(u)=0, whereg is a sufficiently smooth homeomorphism. Particular attention is directed to key parameters which control the iteration. Several examples are given that have been successful in solving the coupled nonlinear PDEs which arise in semiconductor device modelling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398257
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  • 7
    Electronic Resource
    Electronic Resource
    Une méthode numérique pour le calcul des points de retournement. Application à un problème aux limites non-linéaire (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 445-452 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A finite element method (P1) with numerical integration for approximating the boundary value problem −Δu=λe u is considered. It is shown that the discrete problem has a solution branch (with turning point) which converges uniformely to a solution branch of the continuous problem. Error estimates are given; for example it is found that $$\left| {\lambda _0 - \lambda _h^0 } \right| = 0(h^{2 - \varepsilon } )$$ , ɛ〉0, whereλ 0 andλ h 0 are critical values of the parameter λ for continuous and discrete problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400321
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