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

Vyacheslav K.  Isaev; Vyacheslav V. Zolotukhin

doi:10.3934/naco.2013.3.471

Article Contents

2013, Volume 3, Issue 3: 471-489. Doi: 10.3934/naco.2013.3.471

This issue Previous Article Partial Newton methods for a system of equations Next Article Deflating irreducible singular M-matrix algebraic Riccati equations

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

Vyacheslav K. Isaev^1, and
Vyacheslav V. Zolotukhin^2,

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

Received: January 31, 2012

Revised: June 30, 2013

Published: June 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 41A50, 65D07; Secondary: 91A80.

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