On the condition number of some gram matrices arising from least squares approximation in the complex plane

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Abstract

This paper analyses the growth of the condition number of a class of Gram matrices that arise when computing least squares polynomials in polygons of the complex plane. It is shown that if the polygon is inserted between two ellipses then the condition number of the (n+1)×(n+1) Gram matrix is bounded from above by 4 m(n+1)2(k)2 n where m is the number of edges of the polygon, and k≥1 is a known ratio which is close to one if the two ellipses are close to each other.

Original languageEnglish (US)
Pages (from-to)337-347
Number of pages11
JournalNumerische Mathematik
Volume48
Issue number3
DOIs
StatePublished - May 1 1986

Keywords

  • Subject Classifications: AMS(MOS): 65D99, CR: G1.2

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