On the Distribution of Zeros and Poles of Rational Approximants on Intervals
Joint Authors
Blatt, H.-P.
Kovacheva, R. K.
Andrievskii, V. V.
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-05
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
The distribution of zeros and poles of best rational approximants is well understood for the functions f(x)=|x|α, α>0.
If f∈C[−1,1] is not holomorphic on [−1,1], the distribution of the zeros of best rational approximants is governed by the equilibrium measure of [−1,1] under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator.
This phenomenon was discovered first for polynomial approximation.
In this paper, we investigate the asymptotic distribution of zeros, respectively, a-values, and poles of best real rational approximants of degree at most n to a function f∈C[−1,1] that is real-valued, but not holomorphic on [−1,1].
Generalizations to the lower half of the Walsh table are indicated.
American Psychological Association (APA)
Andrievskii, V. V.& Blatt, H.-P.& Kovacheva, R. K.. 2012. On the Distribution of Zeros and Poles of Rational Approximants on Intervals. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-511655
Modern Language Association (MLA)
Andrievskii, V. V.…[et al.]. On the Distribution of Zeros and Poles of Rational Approximants on Intervals. Abstract and Applied Analysis No. 2012 (2012), pp.1-21.
https://search.emarefa.net/detail/BIM-511655
American Medical Association (AMA)
Andrievskii, V. V.& Blatt, H.-P.& Kovacheva, R. K.. On the Distribution of Zeros and Poles of Rational Approximants on Intervals. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-511655
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-511655