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Newton iterations without inverting the DerivativeDedicated to Prof. Dr. H. Görtler on the occasion of his 70th birthday (1979)

Scheurle, J. ; Kirchgässner, K.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 1 (1979), S. 514-529

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Details

ISSN: 0170-4214

Schlagwort(e): Mathematics and Statistics ; Applied Mathematics

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: We describe an iteration procedure in a Banach space which is quadratically convergent like Newton's method. In fact, it is a modification of the latter. The inverted derivatives are replaced by so-called contractors which are constructed recursively. Moreover, this method is extended to a scale of Banach spaces. It turns out that the rate of convergence remains quadratic, even if the norms of the contractors are increasing exponentially. A hard implicit function theorem results. In particular, this theorem can be applied to prove existence of quasiperiodic solutions for the Lorenz model of stationary convection.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/mma.1670010409

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