# American Institute of Mathematical Sciences

2013, 3(3): 471-489. doi: 10.3934/naco.2013.3.471

## Introduction to the theory of splines with an optimal mesh. Linear Chebyshev splines and applications

 1 Prof. N. E. Zhukovsky Central Aerohydrodynamic Institute (TsAGI), Zhukovsky str., 1, Zhukovsky, Moscow region, 140180, Russian Federation 2 Moscow Institute of Physics and Technology (State University) (MIPT), Institutsky Lane 9, Dolgoprudny, Moscow region, 141700, Russian Federation

Received  February 2012 Revised  July 2013 Published  July 2013

On June 18, 2008 at the Plenary Meeting of the International Conference Differential Equations and Topology" dedicated to the 100-th anniversary of L.S. Pontryagin, the report [15] was submitted by Isaev V.K. and Leitmann G. This report in a summary form included a section dedicated to the research of scientists of TsAGI in the field of automation of full life-cycle (i.e. engineering-design-manufacturing, or CAE/CAD/CAM, or CALS-technologies) of wind tunnel models [21]. Within this framework, methods of geometric modeling [1,11] were intensively developed, new classes of optimal splines have been built, including the Pontryagin splines and the Chebyshev splines [12-13,19,37]. This paper reviews some results on the Chebyshev splines. We also give brief remarks about the new applications of Chebyshev splines (outside the usual scope of CALS-technologies in design and manufacturing), namely to the actual problem of air traffic management (ATM) within the Free Flight concept.
Citation: Vyacheslav K. Isaev, Vyacheslav V. Zolotukhin. Introduction to the theory of splines with an optimal mesh. Linear Chebyshev splines and applications. Numerical Algebra, Control and Optimization, 2013, 3 (3) : 471-489. doi: 10.3934/naco.2013.3.471
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