Title: Convergence of modified approximants associated with orthogonal rational functions
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Feb-1995
Publisher: Elsevier science bv
Series Title: Journal of computational and applied mathematics vol:57 issue:1-2 pages:77-86
Abstract: Let {a_n} be a sequence in the unit disk D={z in C: |z| < 1} consisting of a finite number of points cyclically repeated, and let L be the linear space generated by the functions Bn(z)= ∏_{k=1..n} -a_k(z-a_k)/ |a_k |(1- ã_k z). Let {φ_n(z)} be orthogonal rational functions obtained from the sequence {B_n(z)} (orthogonalization with respect to a given functional on L), and let {ψ_n(z)} be the corresponding functions of the second kind (with superstar transforms φ_n^* (z) and ψ_n^*(z), respectively). Interpolation and convergence properties of the modified approximants R_n(z,u_n,v_n) = (u_nψ_n(z)-v_n ψ_n^*(z))/(u_n φ_n(z) +v_nφ_n^*(z)) that satisfy |u_n| = |v_n| are discussed.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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