Controllability of matrix eigenvalue algorithms: The inverse power method

U. Helmke; P. A. Fuhrmann

doi:10.1016/S0167-6911(00)00039-6

Controllability of matrix eigenvalue algorithms: The inverse power method

U. Helmke, P. A. Fuhrmann

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we initiate a program to study the controllability properties of matrix eigenvalue algorithms arising in numerical linear algebra. Our focus is on a well-known eigenvalue method, the inverse power iteration defined on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and sufficient condition for almost controllability of the inverse power method is derived.

Original language	English
Pages (from-to)	57-66
Number of pages	10
Journal	Systems and Control Letters
Volume	41
Issue number	1
DOIs	https://doi.org/10.1016/S0167-6911(00)00039-6
State	Published - 15 Sep 2000

Keywords

Controllability
Eigenvalue method
Invariant subspaces
Projective space

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

Access to Document

10.1016/S0167-6911(00)00039-6

Cite this

@article{a37de6a8388c412a9495017ebccc5ca9,

title = "Controllability of matrix eigenvalue algorithms: The inverse power method",

abstract = "In this paper we initiate a program to study the controllability properties of matrix eigenvalue algorithms arising in numerical linear algebra. Our focus is on a well-known eigenvalue method, the inverse power iteration defined on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and sufficient condition for almost controllability of the inverse power method is derived.",

keywords = "Controllability, Eigenvalue method, Invariant subspaces, Projective space",

author = "U. Helmke and Fuhrmann, {P. A.}",

note = "Funding Information: Partially supported by a grant from the German–Israeli Foundation GIF I-526-034.06/97. ",

year = "2000",

month = sep,

day = "15",

doi = "10.1016/S0167-6911(00)00039-6",

language = "English",

volume = "41",

pages = "57--66",

journal = "Systems and Control Letters",

issn = "0167-6911",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Controllability of matrix eigenvalue algorithms

T2 - The inverse power method

AU - Helmke, U.

AU - Fuhrmann, P. A.

N1 - Funding Information: Partially supported by a grant from the German–Israeli Foundation GIF I-526-034.06/97.

PY - 2000/9/15

Y1 - 2000/9/15

N2 - In this paper we initiate a program to study the controllability properties of matrix eigenvalue algorithms arising in numerical linear algebra. Our focus is on a well-known eigenvalue method, the inverse power iteration defined on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and sufficient condition for almost controllability of the inverse power method is derived.

AB - In this paper we initiate a program to study the controllability properties of matrix eigenvalue algorithms arising in numerical linear algebra. Our focus is on a well-known eigenvalue method, the inverse power iteration defined on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and sufficient condition for almost controllability of the inverse power method is derived.

KW - Controllability

KW - Eigenvalue method

KW - Invariant subspaces

KW - Projective space

UR - http://www.scopus.com/inward/record.url?scp=0004514718&partnerID=8YFLogxK

U2 - 10.1016/S0167-6911(00)00039-6

DO - 10.1016/S0167-6911(00)00039-6

M3 - Article

AN - SCOPUS:0004514718

SN - 0167-6911

VL - 41

SP - 57

EP - 66

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 1

ER -

Controllability of matrix eigenvalue algorithms: The inverse power method

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this