ISSN:
1572-9265
Keywords:
Optimal approximation
;
barycentric formula
;
čebyšev points
;
AMS(MOS) 65D05
;
65D15
;
41A20
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract The barycentric formula has several advantages over other means of evaluating the polynomial interpolating a function betweenn points in an interval. In particular, it is much more stable for sets of points clustered at the extremities of the interval, as are all the sets guaranteeing a good approximation forn sufficiently large. Also, it requires onlyO(n) operations for every function to be interpolated, once some weights, which depend only on the points, have been computed. Computing those weights usually requiresO(n2) operations; for čebyšev points, however,O(n) operations suffice. We show here that all the above is also true for the optimal evaluation of functionals in H2 by giving a closed formula for the corresponding weights.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02215678
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