Zur Berechnung der Rückkehrpunkte von Raumkurven, die implizit durch parameterabhängige nichtlinear Gleichungssysteme definiert werden

Pönisch, Gerd; Schwetlick, Hubert

doi:10.1007/bf02241778

Cited by 63 publications

(30 citation statements)

References 10 publications

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“…Now we are going to relate this parametrization u = Wk('~ ) to that defined by (1), (5), (6). In order to avoid confusion we denote the parameter introduced by (5), (6) for all 1a1<62.…”

Section: The Secant Length Parametrizationmentioning

confidence: 98%

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Parametrization via secant length and application to path following

Menzel

Schwetlick

1985

Numer. Math.

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Summary. A possible way for parametrizing the solution path of the nonlinear system H(u)=0, H: IU+~R" consists of using the secant length as parameter. This idea leads to a quadratic constraint by which the parameter is introduced. A Newton-like method for computing the solution for a given parameter is proposed where the nonlinear system is linearized at each iterate, but the quadratic parametrizing equation is exactly satisfied. The local Q-quadratic convergence of the method is proved and some hints for implementing the algorithm are given

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“…Now we are going to relate this parametrization u = Wk('~ ) to that defined by (1), (5), (6). In order to avoid confusion we denote the parameter introduced by (5), (6) for all 1a1<62.…”

Section: The Secant Length Parametrizationmentioning

confidence: 98%

“…2 where the parameter is called a. The parameter v occurring in (5) is up to sign the secant length between the basic point u k and the point u = Wk(Z ) defined by (1), (5), (6). It represents best the steplength in the k-th step of the path following algorithm.…”

Section: H(u)=0mentioning

confidence: 99%

Parametrization via secant length and application to path following

Menzel

Schwetlick

1985

Numer. Math.

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“…The approach taken here extends to a Banach space setting the results of [13] where a basic procedure was developed that produces characterizations for generalized turning points in finite dimensions. Our approach is related to other characterization equations in special cases such as given in [2,15] and [22]. See [13] and [14].…”

Section: Introductionmentioning

confidence: 99%

“…See, for example, Doedel [9]. The iterative solution of these characterization equations does not require the iterates to lie on the solution manifold as was done in algorithms for simple turning points given by Simpson [26] and also P6nisch and Schwetlick [22].…”

Section: Introductionmentioning

confidence: 99%

The approximation of generalized turning points by projection methods with superconvergence to the critical parameter

Griewank

Reddien

1986

Numer. Math.

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Summary.A procedure is given that generates characterizations of singular manifolds for mildly nonlinear mappings between Banach spaces. This characterization is used to develop a method for determining generalized turning points by using projection methods as a discretization. Applications are given to parameter dependent two-point boundary value problems. In particular, collocation at Gauss points is shown to achieve superconvergence in approximating the parameter at simple turning points.

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“…[23], [24], [27], [29], [31], [32], [34], [39], [40] and the references given there). We shall not go into details here but sketch only some of the principal features of these methods as they apply in the present setting.…”

Section: (Iii)mentioning

confidence: 99%