On the rate of convergence to the neutral attractor of a family of one-dimensional maps

• Autorzy: T. Nowicki , M. Sviridenko , G. Świrszcz , S. Winograd
• Języki publikacji: EN

Abstrakty

EN

For a family of maps
$f_{d}(p) = 1 - (1-p/d)^{d}$, d ∈ [2,∞], p ∈ [0,1].
we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point.

Kategorie tematyczne

• 34D45: Attractors
• 90B80: Discrete location and assignment
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 253-269

Daty

wydano

2009

Twórcy

autor

T. Nowicki

• IBM T. J. Watson Research Center, 1101 Kitchawan Road, PO BOX 218, Yorktown Heights, NY 10598, U.S.A.

autor

M. Sviridenko

• IBM T. J. Watson Research Center, 1101 Kitchawan Road, PO BOX 218, Yorktown Heights, NY 10598, U.S.A.

autor

G. Świrszcz

• IBM T. J. Watson Research Center, 1101 Kitchawan Road, PO BOX 218, Yorktown Heights, NY 10598, U.S.A.

autor

S. Winograd

• IBM T. J. Watson Research Center, 1101 Kitchawan Road, PO BOX 218, Yorktown Heights, NY 10598, U.S.A.

Identyfikatory

DOI

10.4064/fm206-0-14