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Newton interpolation at Leja points


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.

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Research supported in part by NSF under Grant DMS-8704196 and by U.S. Air Force Grant AFSOR-87-0102.

On leave from University of Kentucky, Department of Mathematics, Lexington, KY 40506, U.S.A.

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Reichel, L. Newton interpolation at Leja points. BIT 30, 332–346 (1990).

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AMS(MOS) Subject Classification

  • 65D05

Key words and phrases

  • polynomial interpolaton
  • Newton form
  • stability
  • Leja points
  • ordering of interpolation points