Rational approximation in uniform and weighted L1 norm
نویسندگان
چکیده
منابع مشابه
The best approximation of some rational functions in uniform norm
Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1 + x) and 1/(x − a) where a > 1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this. 2005 IMACS. Published by...
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The author studies the uniform convergence of extended Lagrange interpolation processes based on the zeros of Generalized Laguerre polynomials. 2009 Elsevier Inc. All rights reserved.
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Isotonic regression, the problem of finding values that best fit given observations and conform to specific ordering constraints, has found many applications in biomedical research and other fields. When the constraints form a partial ordering, solving the problem under the L1 error measure takes O(n) when there are n observations. The analysis of large-scale microarray data, which is one of th...
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Let f be holomorphically continuable over the complex plane except for finitely many branch points contained in the unit disk. We prove that best rational approximants to f of degree n, in the L2-sense on the unit circle, have poles that asymptotically distribute according to the equilibrium measure on the compact set outside of which f is single-valued and which has minimal Green capacity in t...
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In [I], a method was given for optimal Hankel-norm approximation with frequency weighting. In a broad sense, this method stands in the same relation to frequency-weighted balanced approximation [2] as unweighted optimal Hankel-norm approximation stands in relation to unweighted balanced approximation, see, e.g. [3]. No bounds were given in [I] on the frequency-domain error associated with frequ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1994
ISSN: 0377-0427
DOI: 10.1016/0377-0427(94)90061-2