Summary: Polynomial perturbations of bilinear functionals
and Hessenberg matrices
, F. Marcellán
Departamento de Matemáticas, Universidad Carlos III de Madrid.
Avenida Universidad, 30. 28911 Leganés. Spain
This paper deals with symmetric and non-symmetric polynomial perturbations of
symmetric quasi-denite bilinear functionals. We establish a relation between the
Hessenberg matrices associated with the initial and the perturbed functionals using
LU and QR factorizations. Moreover we give an explicit algebraic relation between
the sequences of orthogonal polynomials associated with both functionals.
Key words: Perturbation of a bilinear functional, Hessenberg matrix, LU
factorization, QR factorization.
1991 MSC: 42C05, 15A23
Given a linear functional S in the linear space P of polynomials with real
coecients, let us consider the Hankel matrix M = (µi+j)