ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670010409
Permalink
