Fractal approximation of vector functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 69-73.

Voir la notice de l'article provenant de la source Math-Net.Ru

We present a new approach to the approximation of continuous vector-valued functions by fractal interpolative vector-valued ones and find optimal values of their parameters. We illustrate the obtained results with examples.
Mots-clés : fractal interpolation
Keywords: approximation, iterated function systems, attractor.
@article{IVM_2013_11_a5,
     author = {M. F. Davletbaev and K. B. Igudesman},
     title = {Fractal approximation of vector functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {69--73},
     publisher = {mathdoc},
     number = {11},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_11_a5/}
}
TY  - JOUR
AU  - M. F. Davletbaev
AU  - K. B. Igudesman
TI  - Fractal approximation of vector functions
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 69
EP  - 73
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_11_a5/
LA  - ru
ID  - IVM_2013_11_a5
ER  - 
%0 Journal Article
%A M. F. Davletbaev
%A K. B. Igudesman
%T Fractal approximation of vector functions
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 69-73
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_11_a5/
%G ru
%F IVM_2013_11_a5
M. F. Davletbaev; K. B. Igudesman. Fractal approximation of vector functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 69-73. http://geodesic.mathdoc.fr/item/IVM_2013_11_a5/

[1] Barnsley M. F., “Fractal functions and interpolation”, Constructive Approximation, 2 (1986), 303–329 | DOI | MR | Zbl

[2] Massopust P., Interpolation and approximation with splines and fractals, Oxford University Press, Oxford, 2010 | MR | Zbl

[3] Igudesman K., Shabernev G., “Novel method of fractal approximation”, Lobachevskii J. Math., 34:2 (2013), 125–132 | DOI | MR | Zbl

[4] Barnsley M. F., Hurd L. P., Fractal image compression, Wellesley, MA, 1993 | MR

[5] Barnsley M. F., Fractals everywhere, Academic Press Inc., Boston, 1988 | MR | Zbl

[6] Magnus J. R., Neudecker H., Matrix differential calculus with applications in statistics and econometrics, 3rd Ed., John Wiley Sons, Ltd., Chichester, 2007 | MR