Abstract
The algebraic operations described in Chapter 5 are tools for generating linear iterations. In this chapter we discuss how these tools can be used to build new iterative methods. The product of iterations is recalled in Section 7.1 and refers to later applications in Part III. Many traditional iterations are constructed by the additive splitting technique of Section 7.2. The regular splitting and weakly regular splitting defined in §7.2.2 yield sufficient convergence criteria. Another kind of splitting is the P-regular splitting defined in §7.2.4. A special kind of additive splitting is the incomplete triangular decomposition (ILU) discussed in Section 7.3. The transformations introduced in §5.6 will reappear in Section 7.4 under the name preconditioning.
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© 2016 Springer International Publishing Switzerland
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Hackbusch, W. (2016). Genenration of Iterations. In: Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol 95 . Springer, Cham. https://doi.org/10.1007/978-3-319-28483-5_7
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DOI: https://doi.org/10.1007/978-3-319-28483-5_7
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