Rational algorithm for quadratic Christoffel modification and applications to the constrained L²-approximation

Abstract

In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, , where it is allowed z to be in supp(d σ). Also, we present an application of modified algorithm to the measures and , where T ₂(t)=t ²−½ is the second degree monic Chebyshev polynomial of the first kind and , , is the Chebyshev measure of the second kind. Also, we present an application to the constrained L ²-polynomial approximation.

Keywords:

• orthogonal polynomials
• Chebyshev polynomials
• positive measure
• Christoffel algorithm
• three-term recurrence relation
• constrained L ²-approximation

2010 AMS Subject Classifications :

• 33C45
• 33C47
• 41A10
• 41A29
• 65F25