This article is cited in 1 paper

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Criteria and convergence of the focal approximation

T. A. Rakcheeva

Mechanical Engineering Research Institute, RAS, 4 Bardina st., Moscow, 117334, Russia

Abstract: Methods of the solution of a problem of focal approximation — approach on point-by-point given smooth closed empirical curve by multifocal lemniscates are investigated. Criteria and convergence of the developed approached methods with use of the description, both in real, and in complex variables are analyzed. Topological equivalence of the used criteria is proved.

Keywords: curves, approximation, lemniscates, foci, criterion of curves nearness, basic, shape, invariant, algorithm, freedom degrees.

UDC: 519.65

Received: 11.03.2013
Revised: 10.05.2013

DOI: 10.20537/2076-7633-2013-5-3-379-394