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Title: Orthogonal rational functions, associated rational functions and functions of the second kind
Authors: Deckers, Karl ×
Bultheel, Adhemar #
Issue Date: Jul-2008
Publisher: Newswood Limited, International Association of Engineers
Host Document: Proceedings of the World Congress on Engineering 2008 vol:2 pages:838-843
Conference: World Congress on Engineering; Internatl. Conf. of Applied and Engineering Mathematics edition:VII location:London, UK date:2-4 July 2008
Abstract: Consider the sequence of poles A = {α_1,α_2, . . .}, and suppose the rational
functions φ_j with poles in A form an orthonormal system with respect to a Hermitian
positive-definite inner product. Further, assume the φ_j satisfy a three-term recurrence relation.
Let the rational function φ^{(1)}_{j\1}
with poles in {α_2, α_3, . . .} represent the associated
rational function of φ_j of order 1; i.e. the φ_^{(1)}_{j\1} do satisfy the same three-term recurrence
relation as the φ_j . In this paper we then give a relation between φ_j and φ^{(1)}_{j\1} in terms
of the so-called rational functions of the second kind.
Next, under certain conditions on
the poles in A, we prove that the φ^{(1)}_{j\1} form an orthonormal system of rational functions
with respect to a Hermitian positive-definite inner product. Finally, we give a relation between
associated rational functions of different order, independent of whether they form
an orthonormal system.
URI: 
ISBN: 978-988-17012-3-7
Publication status: published
KU Leuven publication type: IC
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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