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Lanczos algorithm on the grassmann manifold
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Orientador(es)
Resumo(s)
The problem of computing eigenvalues, eigenvectors and invariant subspaces is always
present in areas as diverse as Engineering, Physics, Computer Science and
Mathematics. Considering the importance of these problems in many practical
applications, it is not surprising that has been and continues to be the subject of intense
research.
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, 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.
Descrição
5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 8th. World Congress on Computational Mechanics (WCCM8)
Palavras-chave
Invariant subspaces Eigenvectors Lanczos method Eigenvalues Grassmann manifold Stiefel manifold