Lanczos Algorithm on the Grassmann Manifold
Ana Paula Lopes (ISCAP)Ana Julia Viamonte (Universidade Portucalense)
Antonio Jose Pascoal (Universidade Portucalense)
Abstract:
In this paper we developed a new Lanczos algorithm on the
Grassmann manifold. This work comes in the wake of the article by
A. Edelman, T. A. Arias and S. T. Smith, The geometry of
algorithms with orthogonality constraints [EAS98], where they
presented a new conjugate gradient algorithm on the Grassmann and
Stiefel manifolds. These manifolds which are based on
orthogonality constraints, yields penetrating insight into many
numerical algorithms of linear algebra. They have developed an
approach to numerical algorithms involving orthogonality
constraints. As the Lanczos method and the method of conjugate
gradients are closely related, and one of the main problems of the
Lanczos method is the loss of orthogonality, arose the idea of
checking whether it would be possible to get a Lanczos algorithm
on the Grassmann manifold.
Keywords:
Numerical Algorithms for CS&E
