Condition Number of Modified Moment Matrices Arising from Least Squares Approximation in the Complex Plane

摘要

This paper analyses the growth of the condition number of a class of modified moment 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) x (n+1) modified moment matrix is upper bounded by 2m(n+1) squared (k)2n power, where m is the number of edges of the polygon, and k > or = 1 is a known ratio which is close to one if the two ellipses are close to each other.