Newton interpolation at Leja points

Lothar Reichel

doi:10.1007/BF02017352

BIT

June 1990, Volume 30, Issue 2, pp 332–346

Newton interpolation at Leja points

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Lothar Reichel

Part II Numerical Mathematics

Received:: 15 May 1989
Revised:: 15 August 1989

DOI: 10.1007/BF02017352

Cite this article as:: Reichel, L. BIT (1990) 30: 332. doi:10.1007/BF02017352

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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.

AMS(MOS) Subject Classification

65D05

Key words and phrases

polynomial interpolaton Newton form stability Leja points ordering of interpolation points

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Lothar Reichel
- 1

1.Bergen Scientific CentreBergenNorway

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Newton interpolation at Leja points

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