liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Adaptive eigenvalue computations using Newton's method on the Grassmann manifold
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.ORCID iD: 0000-0003-2281-856X
2002 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, Vol. 23, no 3, 819-839 p.Article in journal (Refereed) Published
Abstract [en]

We consider the problem of updating an invariant subspace of a large and structured Hermitian matrix when the matrix is modified slightly. The problem can be formulated as that of computing stationary values of a certain function with orthogonality constraints. The constraint is formulated as the requirement that the solution must be on the Grassmann manifold, and Newton's method on the manifold is used. In each Newton iteration a Sylvester equation is to be solved. We discuss the properties of the Sylvester equation and conclude that for large problems preconditioned iterative methods can be used. Preconditioning techniques are discussed. Numerical examples from signal subspace computations are given in which the matrix is Toeplitz and we compute a partial singular value decomposition corresponding to the largest singular values. Further we solve numerically the problem of computing the smallest eigenvalues and corresponding eigenvectors of a large sparse matrix that has been slightly modified.

Place, publisher, year, edition, pages
2002. Vol. 23, no 3, 819-839 p.
Keyword [en]
Conjugate gradient method, Differential geometry, Eigenvalue, Eigenvector, Grassmann manifold, Newton's method, Preconditioner, Signal subspace problem, Singular values and vectors, Sparse matrix, Toeplitz matrix
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-47142DOI: 10.1137/S0895479899354688OAI: diva2:268038
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-08-30

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Elden, Lars
By organisation
The Institute of TechnologyScientific Computing
In the same journal
SIAM Journal on Matrix Analysis and Applications
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 310 hits
ReferencesLink to record
Permanent link

Direct link