Abstract
Incomplete Choleski decompositions and modified versions thereof are quite effective preconditioners for the conjugate gradients method. It is explained why Modified Incomplete Choleski may lead to more iteration steps, in some cases, whereas it should theoretically be more effective than standard Incomplete Choleski. It is also shown, by carefully analyzing a numerical example, why the convergence behaviour of Conjugate Gradients-Squared can be, sometimes unacceptable, irregular.
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Van der Vorst, H.A. (1990). The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors. In: Axelsson, O., Kolotilina, L.Y. (eds) Preconditioned Conjugate Gradient Methods. Lecture Notes in Mathematics, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090905
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DOI: https://doi.org/10.1007/BFb0090905
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