A canonical Geronimus transformation for matrix orthogonal polynomials Articles uri icon

publication date

  • February 2018

start page

  • 357

end page

  • 381

issue

  • 2

volume

  • 66

International Standard Serial Number (ISSN)

  • 0308-1087

Electronic International Standard Serial Number (EISSN)

  • 1563-5139

abstract

  • We consider matrix polynomials orthogonal with respect to a sesquilinear form where is a symmetric, positive definite matrix of measures supported in some infinite subset of the real line, and W(t) is a matrix polynomial of degree 1. We obtain a connection formula between the sequences of matrix polynomials orthogonal with respect to and as well as a relation between the corresponding block Jacobi matrices. A non-symmetric sesquilinear form is also considered.

keywords

  • matrix orthogonal polynomials; block jacobi matrices; matrix geronimus transformation; block cholesky decomposition; block lu decomposition