The geometry of algorithms with orthogonality constraints. (English) Zbl 0928.65050

Edelman, Alan; Arias, Tomás A.; Smith, Steven T.

SIAM J. Matrix Anal. Appl. 20, No. 2, 303-353 (1998).

The paper offers a new approach to the algorithms in numerical analysis involving orthogonality constraints. As a concluding example of the insight gained, a Grassmann based taxonomy for problems related to the symmetric eigenproblem is proposed. Some Newton and conjugate gradient methods are developed on the Grassmann and Stiefel manifolds that arise in such areas as symmetric or nonlinear eigenvalue problem. The theory proposed provides a taxonomy for numerical linear algebra algorithms that gives a top level mathematical view of many algorithms.

Reviewer: D.Petcu (Timişoara)

MSC:

65F15	Numerical computation of eigenvalues and eigenvectors of matrices
81V55	Molecular physics

Keywords:

orthogonality constraints; Newton method; symmetric eigenproblem; conjugate gradient methods; Grassmann and Stiefel manifolds; nonlinear eigenvalue problem; algorithms

Software:

JDQZ