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

Youcef Saad

doi:10.1007/BF01389479

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

Youcef Saad

Computer Science and Engineering

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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 language	English (US)
Pages (from-to)	337-347
Number of pages	11
Journal	Numerische Mathematik
Volume	48
Issue number	3
DOIs	https://doi.org/10.1007/BF01389479
State	Published - May 1986

Keywords

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

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10.1007/BF01389479

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AB - 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.

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

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