New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction

T. Nigel Lucas

Research output: Contribution to journal › Article

5 Citations (Scopus)

Abstract

Three well-known stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation method—are consequently shown to be closely related. Previously observed properties of the methods are explained by treating them as multipoint approximants, and the significance of using expansion points on the imaginary axis is shown to be central to stability preservation.
Original languageEnglish
Pages (from-to)1267-1274
Number of pages8
JournalInternational Journal of Systems Science
Volume20
Issue number7
DOIs
Publication statusPublished - 1989

Fingerprint

Model Reduction
Approximation
Padé Approximation
Preservation
Relationships
Form

Cite this

Lucas, T. Nigel. / New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction. In: International Journal of Systems Science. 1989 ; Vol. 20, No. 7. pp. 1267-1274.
@article{2e0ee12cb02f433e8349df882e2dcb72,
title = "New results on relationships between multipoint Pad{\'e} approximation and stability preserving methods in model reduction",
abstract = "Three well-known stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation method—are consequently shown to be closely related. Previously observed properties of the methods are explained by treating them as multipoint approximants, and the significance of using expansion points on the imaginary axis is shown to be central to stability preservation.",
author = "Lucas, {T. Nigel}",
year = "1989",
doi = "10.1080/00207728908910211",
language = "English",
volume = "20",
pages = "1267--1274",
journal = "International Journal of Systems Science",
issn = "0020-7721",
publisher = "Taylor and Francis Ltd.",
number = "7",

}

Lucas, TN 1989, 'New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction', International Journal of Systems Science, vol. 20, no. 7, pp. 1267-1274. https://doi.org/10.1080/00207728908910211

New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction. / Lucas, T. Nigel.

In: International Journal of Systems Science, Vol. 20, No. 7, 1989, p. 1267-1274.

Research output: Contribution to journal › Article

TY - JOUR

T1 - New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction

AU - Lucas, T. Nigel

PY - 1989

Y1 - 1989

N2 - Three well-known stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation method—are consequently shown to be closely related. Previously observed properties of the methods are explained by treating them as multipoint approximants, and the significance of using expansion points on the imaginary axis is shown to be central to stability preservation.

AB - Three well-known stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation method—are consequently shown to be closely related. Previously observed properties of the methods are explained by treating them as multipoint approximants, and the significance of using expansion points on the imaginary axis is shown to be central to stability preservation.

U2 - 10.1080/00207728908910211

DO - 10.1080/00207728908910211

M3 - Article

VL - 20

SP - 1267

EP - 1274

JO - International Journal of Systems Science

JF - International Journal of Systems Science

SN - 0020-7721

IS - 7

ER -

Lucas TN. New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction. International Journal of Systems Science. 1989;20(7):1267-1274. https://doi.org/10.1080/00207728908910211

Access to Document