Electronic Resource
Springer
BIT
30 (1990), S. 332-346
ISSN:
1572-9125
Keywords:
65D05
;
polynomial interpolaton
;
Newton form
;
stability
;
Leja points
;
ordering of interpolation points
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The Newton form is a convenient representation for interpolation polynomials. Its sensitivity to perturbations depends on the distribution and ordering of the interpolation points. The present paper bounds the growth of the condition number of the Newton form when the interpolation points are Leja points for fairly general compact sets K in the complex plane. Because the Leja points are defined recursively, they are attractive to use with the Newton form. If K is an interval, then the Leja points are distributed roughly like Chebyshev points. Our investigation of the Newton form defined by interpolation at Leja points suggests an ordering scheme for arbitrary interpolation points.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02017352
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