Electronic Resource
Springer
Numerische Mathematik
53 (1988), S. 411-422
ISSN:
0945-3245
Keywords:
AMS(MOS): 65 D 15
;
CR: G 1.2
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary The approximability of a real analytic function on the standard interval [−1, 1] by polynomials depends essentially only on the size of its ellipse of analyticity. If the interval is subdivided byn+1 points, the same holds for each subinterval. For a fixed singularity, it becomes a purely geometric question to find how the partition has to be chosen such that the worst rate of approximation attains its minimum. We prove that for anyn their exists a unique optimal partition, which solves a nonlinear difference equation. We give an asymptotic expression for it.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01396326
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