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Vector-Orthogonality and Lanczos-Type Methods

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Abstract

A method for solving a linear system is defined. It is a Lanczos-type method, but it uses formal vector orthogonality instead of scalar orthogonality. Moreover, the dimension of vector orthogonality may vary which gives a large freedom in leading the algorithm, and controlling the numerical problems. The ideas of truncated and restarted methods are revisited. The obtained residuals are exactly orthogonal to a space of increasing dimension. Some experiments are done, the problem of finding automaticaly good directions of projection remains partly open.

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Authors and Affiliations

  1. UFR de Mathématiques, Université de Lille, 59655, Villeneuve d'Ascq Cedex, France

    Jeannette Van Iseghem

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  1. Jeannette Van Iseghem
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Van Iseghem, J. Vector-Orthogonality and Lanczos-Type Methods. Numerical Algorithms 29, 267–279 (2002). https://doi.org/10.1023/A:1014836728675

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  • DOI: https://doi.org/10.1023/A:1014836728675

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