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A new perspective on the fictitious space lemma

In the present contribution we propose a new proof of the so-called fictitious space lemma. For the proof, we exhibit an explicit expression for the inverse of additive Schwarz preconditioners in terms of Moore-Penrose pseudo inverse of the map associated to the decomposition over the subdomain partition.

preprint2022arXivOpen access
Xavier Claeys
math.NANumerical Analysis
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Xavier Claeys

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