Vol.4, No 17, 2005 pp. 279-285
UDC 517.518.82+517.538(045)=20
ITERATIVE PROCESSES AND PADÉ
APPROXIMANTS
I. V. Andrianov1, J. Awrejcewicz2,
G. Kudra2
1Institut für Allgemeine Mechanik,
RWTH Aachen, Templergraben 64,
D-52056, Aachen, Germany
2Technical University of Łódź,
Department
of Automatics and Biomechanics,
1/15 Stefanowski St., 90-924 Łódź, Poland
Abstract. In many application oriented researches the initial
coefficients
characterizng a discontinuity of the governing differential equations
(for
instance, caused by the dry friction) are often substituted by the
continuous
functions (approximations). One of the effective methods to use the
described
methodology is that related to introducing a formal small
(perturbation)
parameter, and then to carry out the successive iterations due to this
parameter. In this paper we show, that a combination of the mentioned
iterative
procedure with the Padé approximants leads to a drastic decrease of the
number of iterations.
Key words: iterative processes, Padé approximations
ITERATIVNI PROCESI I PADÉ-OVA
APROKSIMACIJA
U mnogim istraživanjima orjentisanim ka primeni, početni koeficijenti
koji
karakterišu diferencijalne jednačine (uzrokovani npr. trenjem) često se
zamenjuju kontinualnim funkcijama (aproksimacija). Jedan od efektivnih
metoda za korišćenje opisane metodologije zasniva se na uvođenju
formalno
malog (preturbacionog) parametra, a zatim na izvođenju sukcesivnih
iteracija
po ovom parametru. U ovom radu pokazali smo da kombinacija pomenute
iterativne
procedure i Padé-ove aproksimacije vodi ka značajnom smanjenju broja
iteracija.
Ključne reči: iterativni procesi, Padé-ova aproksimacija.
