Notes on linear factor polynomial deflation in polynomial bases

Scalar polynomials as approximations to more general scalar functions lead to the study of scalar polynomials represented in a variety of classical systems of polynomials, including orthogonal systems and Lagrange polynomials, for example. This article, motivated in part by analogy with the existing methods for linear factor polynomial deflation in the monomial basis, finds forward and backward deflation formulae for several such representations. It also finds the sensitivity factor of the deflation process for each representation.