Generalized biorthogonal bases and tridiagonalisation of matrices |
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| Authors: | Markus Ziegler |
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| Affiliation: | Mathematische Institut, Biomathematik, Universit?t Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany, email: markus.ziegler@uni-tuebingen.de, DE
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| Abstract: | Summary. In connection with the breakdown problem of the Lanczos algorithm a theory of generalized biorthogonal bases is developed. The connection between the generalized biorthogonal bases of Krylov chains and look-ahead Lanczos recursions is worked out in detail. It is shown how generalized biorthogonal bases with “antidiagonal blocks” can be constructed with small computational effort. Finally a special look-ahead Lanczos algorithm is derived which requires minimal computational effort and storage. Received September 21, 1995 / Revised version received August 12, 1996 |
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| Keywords: | Mathematics Subject Classification (1991): 65F15 93B10 93C75 |
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