, Volume 48, Issue 3, pp 337-347

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

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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 4m(n+1)2(k)2n wherem is the number of edges of the polygon, andk≥1 is a known ratio which is close to one if the two ellipses are close to each other.

This work was supported in part by the U.S. Office of Naval Research under grant N00014-82-K-0184, in part by Dept. Of Energy under Grant AC02-81ER10996, and in part by Army Research Office under contract DAAG-83-0177