4. Appendix: theoretical additions to contraction analysis

4.1 Preliminary concepts

We have seen in [AF 1 385] the importance of strongly diagonal dominant matrices for analyzing the behavior of asynchronous parallel algorithms. In this appendix, we illustrate the link between these strongly diagonal-dominant matrices and a notion of accreteness that extends the notion of monotonicity to the case of normed vector spaces, restricting it to the case where the space is normed by the norm of the maximum.

Let U be a vector...

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Appendix: theoretical additions to contraction analysis

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Bibliography

(1) - ARNAL (J.), MIGALLÓN (V.), PENADÉS (J.) - Non-stationary parallel multisplitting algorithms for almost linear systems. - In: Numer. Linear Algebra Appl. 6, p. 79–92 (1999).
(2) - BAHI (J.), MIELLOU (J.-C.), RHOFIR (K.) - Asynchronous Multisplitting...