Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle

Adhemar Bultheel ; Ruyman Cruz-Barroso ; Andreas Lasarow

Symmetry, integrability and geometry: methods and applications, Tome 13 (2017)

Résumé

Orthogonal rational functions (ORF) on the unit circle generalize orthogonal polynomials (poles at infinity) and Laurent polynomials (poles at zero and infinity). In this paper we investigate the properties of and the relation between these ORF when the poles are all outside or all inside the unit disk, or when they can be anywhere in the extended complex plane outside the unit circle. Some properties of matrices that are the product of elementary unitary transformations will be proved and some connections with related algorithms for direct and inverse eigenvalue problems will be explained.

Détail

Keywords: orthogonal rational functions; rational Szegő quadrature; spectral method; rational Krylov method; AMPD matrix.

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