A differential-geometric look at the Jacobi-Davidson framework

P.A. Absil; M.E. Hochstenbach

A differential-geometric look at the Jacobi-Davidson framework

Scientific Computing

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

Abstract

The problem of computing a p-dimensional invariant subspace of a symmetric positive-definite matrix pencil of dimension n is interpreted as computing a zero of a tangent vector field on the Grassmann manifold of p-planes in Rn. The theory of Newton’s method on manifolds is applied to this problem, and the resulting Newton equations are interpreted as block versions of the Jacobi–Davidson correction equation for the generalized eigenvalue problem.

Original language	English
Title of host publication	Mathematical system theory : Festschrift in honor of Uwe Helmke on the occasion of his sixtieth birthday
Editors	K. Hüper, J. Trumpf
Publisher	CreateSpace
Pages	11-21
ISBN (Print)	978-1470044008
Publication status	Published - 2013

Cite this

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title = "A differential-geometric look at the Jacobi-Davidson framework",

abstract = "The problem of computing a p-dimensional invariant subspace of a symmetric positive-definite matrix pencil of dimension n is interpreted as computing a zero of a tangent vector field on the Grassmann manifold of p-planes in Rn. The theory of Newton{\textquoteright}s method on manifolds is applied to this problem, and the resulting Newton equations are interpreted as block versions of the Jacobi–Davidson correction equation for the generalized eigenvalue problem.",

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AB - The problem of computing a p-dimensional invariant subspace of a symmetric positive-definite matrix pencil of dimension n is interpreted as computing a zero of a tangent vector field on the Grassmann manifold of p-planes in Rn. The theory of Newton’s method on manifolds is applied to this problem, and the resulting Newton equations are interpreted as block versions of the Jacobi–Davidson correction equation for the generalized eigenvalue problem.

M3 - Chapter

SN - 978-1470044008

SP - 11

EP - 21

BT - Mathematical system theory : Festschrift in honor of Uwe Helmke on the occasion of his sixtieth birthday

A2 - Hüper, K.

A2 - Trumpf, J.

PB - CreateSpace

ER -

A differential-geometric look at the Jacobi-Davidson framework

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