Title: Quadratures associated with pseudo-orthogonal rational functions on the real half line with poles in [-∞,0]
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Jan-2013
Publisher: Elsevier
Series Title: Journal of Computational and Applied Mathematics vol:237 issue:1 pages:589-602
Abstract: We consider a positive measure on [0,∞) and a sequence of nested spaces ℒ_0 ⊂ ℒ_1 ⊂ ℒ_2 ... of rational functions with prescribed poles in [-∞,0]. Let {φ_k : k = 0..∞}, with φ_0 ∈ ℒ_0 and φ_k ∈ ℒ_k ∖ ℒ_{k-1}, k = 1,2,... be the associated sequence of orthogonal rational functions. The zeros of φ_n can be used as the nodes of a rational Gauss quadrature formula that is exact for all functions in ℒ_n . ℒ_{n-1}, a space of dimension 2n. Quasi- and pseudo-orthogonal functions are functions in ℒ_n that are orthogonal to some subspace of ℒ_{n-1}. Both of them are generated from φ_n and φ_{n-1} and depend on a real parameter τ. Their zeros can be used as the nodes of a rational Gauss-Radau quadrature formula where one node is fixed in advance and the others are chosen to maximize the subspace of ℒ_n . ℒ_{n-1} where the quadrature is exact. The parameter τ is used to fix a node at a pre-assigned point. The space where the quadratures are exact has dimension 2n-1 in both cases but it is in ℒ_{n-1} . ℒ_{n-1} in the quasi-orthogonal case and it is in ℒ_n . ℒ_{n-2} in the pseudo-orthogonal case.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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