Extremal polynomials on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e25" altimg="si15.svg"><mml:mi>n</mml:mi></mml:math>-grid
نویسندگان
چکیده
The n-grid En consists of n equally spaced points in [−1,1] including the endpoints ±1. extremal polynomial pn∗ is that maximizes uniform norm ‖p‖[−1,1] among polynomials p degree ≤αn are bounded by one absolute value on En. For every α∈(0,1), we determine limit 1nlog‖pn∗‖[−1,1] as n→∞. interest this comes from a connection with an impossibility theorem stable approximation n-grid.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2023
ISSN: ['0021-9045', '1096-0430']
DOI: https://doi.org/10.1016/j.jat.2023.105875