Abstract
The Lanczos algorithm, originally devised to tridiagonalize a matrix, is used for the generalized eigenvalue problem to operate on a whole subspace, yielding a block-tridiagonal matrix in the Krylov sequence of subspaces. To use prior information and enhance convergence, a subspace restart formulation is introduced. Global orthogonality of the iterated vectors is maintained by a double Gram-Schmidt re-orthogonalization.
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© 1987 Birkhäuser Verlag Basel
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Matthies, H.G. (1987). A Lanczos Algorithm with Restarts. In: Albrecht, J., Collatz, L., Velte, W., Wunderlich, W. (eds) Numerical Treatment of Eigenvalue Problems Vol.4 / Numerische Behandlung von Eigenwertaufgaben Band 4. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 83. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7507-3_13
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DOI: https://doi.org/10.1007/978-3-0348-7507-3_13
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