Continuous-time subspace flows related to the symmetric eigenproblem

P. A. Absil; R. Sepulchre; R. Mahony

Continuous-time subspace flows related to the symmetric eigenproblem

P. A. Absil^*
, R. Sepulchre
, R. Mahony

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

3 Citations (Scopus)

Abstract

The classes of continuous-time flows on R^n×p that induce the same flow on the set of p- dimensional subspaces of R^n×p are described. The power flow is briefly reviewed in this framework, and a subspace generalization of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003, pp. 343-357] is proposed and analyzed. This new flow displays a property akin to deflation in finite time.

Original language	English
Pages (from-to)	179-194
Number of pages	16
Journal	Pacific Journal of Optimization
Volume	4
Issue number	2
Publication status	Published - May 2008

Cite this

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title = "Continuous-time subspace flows related to the symmetric eigenproblem",

abstract = "The classes of continuous-time flows on Rn×p that induce the same flow on the set of p- dimensional subspaces of Rn×p are described. The power flow is briefly reviewed in this framework, and a subspace generalization of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003, pp. 343-357] is proposed and analyzed. This new flow displays a property akin to deflation in finite time.",

keywords = "Finite-time deflation, Grassmann Rayleigh quotient flow, Invariant subspace, Matrix flows, Power flow, Principal component analysis, Subspace flows",

author = "Absil, \{P. A.\} and R. Sepulchre and R. Mahony",

year = "2008",

month = may,

language = "English",

volume = "4",

pages = "179--194",

journal = "Pacific Journal of Optimization",

issn = "1348-9151",

publisher = "Yokohama Publications",

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T1 - Continuous-time subspace flows related to the symmetric eigenproblem

AU - Absil, P. A.

AU - Sepulchre, R.

AU - Mahony, R.

PY - 2008/5

Y1 - 2008/5

N2 - The classes of continuous-time flows on Rn×p that induce the same flow on the set of p- dimensional subspaces of Rn×p are described. The power flow is briefly reviewed in this framework, and a subspace generalization of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003, pp. 343-357] is proposed and analyzed. This new flow displays a property akin to deflation in finite time.

AB - The classes of continuous-time flows on Rn×p that induce the same flow on the set of p- dimensional subspaces of Rn×p are described. The power flow is briefly reviewed in this framework, and a subspace generalization of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003, pp. 343-357] is proposed and analyzed. This new flow displays a property akin to deflation in finite time.

KW - Finite-time deflation

KW - Grassmann Rayleigh quotient flow

KW - Invariant subspace

KW - Matrix flows

KW - Power flow

KW - Principal component analysis

KW - Subspace flows

UR - https://www.scopus.com/pages/publications/72249110258

M3 - Review article

SN - 1348-9151

VL - 4

SP - 179

EP - 194

JO - Pacific Journal of Optimization

JF - Pacific Journal of Optimization

IS - 2

ER -

Continuous-time subspace flows related to the symmetric eigenproblem

Abstract

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