Cubically convergent iterations for invariant subspace computation

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

doi:10.1137/S0895479803422002

Cubically convergent iterations for invariant subspace computation

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

^*Corresponding author for this work

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

23 Citations (Scopus)

Abstract

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ ⁿ and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

Original language	English
Pages (from-to)	70-96
Number of pages	27
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	26
Issue number	1
DOIs	https://doi.org/10.1137/S0895479803422002
Publication status	Published - 2005

Access to Document

10.1137/S0895479803422002

Cite this

@article{dc37d1c3a65e4dbba812a79cebd6c69f,

title = "Cubically convergent iterations for invariant subspace computation",

abstract = "We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.",

keywords = "Cubic convergence, Global convergence, Grassmann manifold, Invariant subspace, Inverse iteration, Newton method, Rayleigh quotient, Symmetric eigenproblem",

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

year = "2005",

doi = "10.1137/S0895479803422002",

language = "English",

volume = "26",

pages = "70--96",

journal = "SIAM Journal on Matrix Analysis and Applications",

issn = "0895-4798",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - Cubically convergent iterations for invariant subspace computation

AU - Absil, P. A.

AU - Sepulchre, R.

AU - Van Dooren, P.

AU - Mahony, R.

PY - 2005

Y1 - 2005

N2 - We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

AB - We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

KW - Cubic convergence

KW - Global convergence

KW - Grassmann manifold

KW - Invariant subspace

KW - Inverse iteration

KW - Newton method

KW - Rayleigh quotient

KW - Symmetric eigenproblem

UR - http://www.scopus.com/inward/record.url?scp=14544282521&partnerID=8YFLogxK

U2 - 10.1137/S0895479803422002

DO - 10.1137/S0895479803422002

M3 - Article

SN - 0895-4798

VL - 26

SP - 70

EP - 96

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 1

ER -

Cubically convergent iterations for invariant subspace computation

Abstract

Access to Document

Other files and links

Fingerprint

Cite this