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2. A differential-geometric look at the Jacobi-Davidson framework

Author

Absil, P.A., Hochstenbach, M.E., and Scientific Computing

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 R^n. 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.

Published
2012

3. A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces.

Author

Absil, P.A., Mahony, R., Sepulchre, R., and Van Dooren, P.

Subjects
*RAYLEIGH quotient, *MATRICES (Mathematics), *AUSDEHNUNGSLEHRE
Abstract

Proposes a generalization of the classical Rayleigh quotient iteration (RQI) which computes p-dimensional invariant subspace of A. Review of the classical RQI; Representation of p-dimensional subspaces by means of matrices and an associated measure of distance between subspaces; Convergence of the Grassmann-RQI; Comparison with other Grassmannian methods.

Published
2002
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