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Computation of bounded degree Nevanlinna-Pick interpolants by solving nonlinear equationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2003 (English)In: 42nd IEEE Conference on Decision and Control: Maui, HI, DEC 09-12, 2003, 2003, 4511-4516 p.Conference paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

2003. 4511-4516 p.
##### Keyword [en]

Nevanlinna-Pick interpolation, positive realness, rationality, system of nonlinear equations, continuation method
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-14162DOI: 10.1109/CDC.2003.1272255ISI: 000189434100774ISBN: 0-7803-7924-1OAI: oai:DiVA.org:kth-14162DiVA: diva2:331168
#####

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#####

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##### Note

QC 20100721Available from: 2010-07-21 Created: 2010-07-21 Last updated: 2010-07-21Bibliographically approved
##### In thesis

This paper provides a procedure for computing scalar real rational Nevanlinna-Pick interpolants of a bounded degree. It applies to a wider class of interpolation problems and seems numerically more reliable than previous, optimization-based, procedures. It is based on the existence and the uniqueness of the solution guaranteed by Georgiou's proof of bijectivity of a map between a class of nonnegative trigonometric polynomials and a class of numerator/denominator polynomial pairs of interpolants. Further analysis of this map suggests a numerical continuation method for determining the interpolant from a system of nonlinear equations. A numerical example illustrates the reliability of the proposed procedure.

1. Modeling and Model Reduction by Analytic Interpolation and Optimization$(function(){PrimeFaces.cw("OverlayPanel","overlay24306",{id:"formSmash:j_idt731:0:j_idt735",widgetVar:"overlay24306",target:"formSmash:j_idt731:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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