Uniform estimate for a segment function in terms of a polynomial strip
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S. I. Dudov and E. V. Sorina
Translated by: A. Plotkin - St. Petersburg Math. J. 24 (2013), 723-742
- DOI: https://doi.org/10.1090/S1061-0022-2013-01262-3
- Published electronically: July 24, 2013
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Abstract:
A problem about a uniform estimate for a continuous segment function in terms of a polynomial strip is considered. The problem reduces to a convex programming problem the target function of which is equal to the sum of the target functions for the inner and outer estimate of the same segment function via a polynomial strip. Convex analysis tools are used to obtain necessary and sufficient conditions for being a solution, and also uniqueness conditions in a form resembling the Chebyshov alternance.References
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Bibliographic Information
- S. I. Dudov
- Affiliation: Saratov state university, Astrakhanskaya str. 83, Saratov 410012, Russia
- Email: DudovSI@info.sgu.ru
- E. V. Sorina
- Affiliation: Saratov state university, Astrakhanskaya str. 83, Saratov 410012, Russia
- Email: sorina@rol.ru
- Received by editor(s): September 9, 2011
- Published electronically: July 24, 2013
- Additional Notes: The author was supported by RFBR (grant no. 10-01-00270-a) and by the NSh grant NSh-4383.2010.1.
- © Copyright 2013 American Mathematical Society
- Journal: St. Petersburg Math. J. 24 (2013), 723-742
- MSC (2010): Primary 90C05
- DOI: https://doi.org/10.1090/S1061-0022-2013-01262-3
- MathSciNet review: 3087820