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

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10.1016/S0167-6911(00)00039-6

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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",

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

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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 - https://www.scopus.com/pages/publications/0004514718

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

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

M3 - Article

AN - SCOPUS:0004514718

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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

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