Titlebook: Iterative Solution of Large Sparse Systems of Equations; Wolfgang Hackbusch Book 19941st edition Springer-Verlag New York, Inc. 1994 Canon

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织物

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Analysis for M-Matrices,The positive definiteness A > 0 establishes a partial-order relation in the algebra of the Hermitian matrices. . order relation in the algebra of all real matrices is defined by elementwise inequalities: . In this chapter, we use the signs «>» and «≥» only in the componentwise sense (1a, b).

Flagging

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富饶

Domain Decomposition Methods,Various iterative methods can be classified as domain decomposition methods. Although a prototype of this iteration due to H. A. Schwarz (Viertelsjahresschrift der Naturforschenden Gesellschaft in Zürich, Vol. 15, 1870) is already 120 years old, this class of algorithms has attracted the interest of numerical analysts only recently.

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Semi-Iterative Methods,Assume that for a starting iterate ., the iterates . are computed. Up to now, the last computed iterate . has been regarded as the result of an iteration Φ. The previously calculated . (0 ≤ . ≤ . − 1) are forgotten.

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Transformations, Secondary Iterations, Incomplete Triangular Decompositions,ucing new features. Techniques of the former kind are the transformations described in §§8.1–3 and the composed methods from §8.4 generated by a secondary iteration, whereas the ILU decomposition from §8.5 is of the latter kind, since it produces a new method.

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