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On Bernstein type inequalities and a weighted Chebyshev approximation problem on ellipsesA classical inequality due to Bernstein which estimates the norm of polynomials on any given ellipse in terms of their norm on any smaller ellipse with the same foci is examined. For the uniform and a certain weighted uniform norm, and for the case that the two ellipses are not too close, sharp estimates of this type were derived and the corresponding extremal polynomials were determined. These Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. Some new results were also presented for a weighted approximation problem of this type.
Document ID
19900014695
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Freund, Roland (Wuerzburg Univ. Germany, F.R. , United States)
Date Acquired
September 6, 2013
Publication Date
May 1, 1989
Subject Category
Numerical Analysis
Report/Patent Number
RIACS-TR-89.21
NASA-CR-180368
NAS 1.26:180368
Accession Number
90N24011
Funding Number(s)
CONTRACT_GRANT: NCC2-387
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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