Vector-Orthogonality and Lanczos-Type Methods |
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Authors: | Jeannette Van Iseghem |
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Institution: | (1) UFR de Mathématiques, Université de Lille, 59655 Villeneuve d'Ascq Cedex, France |
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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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Keywords: | Lanczos-type methods for linear systems vector orthogonality |
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