New block Lanczos algorithm. (English) Zbl 1338.65102

Harkiolakis, Nikos (ed.) et al., Advances in applied mathematics, systems, communications and computers. Selected papers based on the presentations at the conferences on communications & information technology 2008, circuits, systems and signals 2008 and applied mathematics, simulation, modelling 2008, Marathon Beach, Attica, Greece, June 1–3, 2008. [s.l.]: North Atlantic University Union (NAUN) (ISBN 978-960-6766-69-5). 42-43 (2011).
Summary: We developed a new Lanczos algorithm on the Grassman manifold. This work comes in the wake of the article by A. Edelman, T. A. Arias and S. T. Smith [SIAM J. Matrix Anal. Appl. 20, No. 2, 303–353 (1998; Zbl 0928.65050)], where they presented a new conjugate gradient algorithm on the Grassman 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 Grassman manifold.
For the entire collection see [Zbl 1222.94002].


65F15 Numerical computation of eigenvalues and eigenvectors of matrices


Zbl 0928.65050