Rational algorithm for quadratic Christoffel modification and applications to the constrained L 2-approximation

In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, dσ̂ (t) = (t − z)2 dσ(t), where it is allowed z to be in supp(dσ).Also, we present an application of modified algorithm to the measures dσ̂ (t) = T 2 2 (t) dσ(t) and dσ ′(t) = t2T 2 2 (t) dσ(t), where T2(t) = t2 − 1 2 is the second degree monic Chebyshev polynomial of the first kind and dσ(t) = √1 − t2 dt , t ∈ [−1, 1], is the Chebyshev measure of the second kind. Also, we present an application to the constrained L2-polynomial approximation.