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On the Critical Lengths of Cycloidal Spaces

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Abstract

The cycloidal spaces C n , generated by the trigonometric polynomials of degree 1 and algebraic polynomials of degree n−2, have important applications in computer-aided geometric design. The critical length of C n is the supremum of the lengths of the intervals on which C n is an extended Chebyshev space. We provide a constructive procedure to obtain the critical lengths of the spaces C n .

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Acknowledgements

The authors are partially supported by MTM2012-31544 Spanish Research Grant by Gobierno de Aragón and Fondo Social Europeo.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, 50009, Zaragoza, Spain

    J. M. Carnicer, E. Mainar & J. M. Peña

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  1. J. M. Carnicer
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  2. E. Mainar
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  3. J. M. Peña
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Correspondence to J. M. Carnicer.

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Communicated by Wolfgang Dahmen.

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Carnicer, J.M., Mainar, E. & Peña, J.M. On the Critical Lengths of Cycloidal Spaces. Constr Approx 39, 573–583 (2014). https://doi.org/10.1007/s00365-013-9223-1

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  • DOI: https://doi.org/10.1007/s00365-013-9223-1

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