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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the abstract additive Schwarz method, named after Hermann Schwarz, is an abstract version of the additive Schwarz method, formulated only in terms of linear algebra without reference to domains, subdomains, etc. Many if not all domain decomposition methods can be cast as abstract additive Schwarz method, which is often the first and most convenient approach to their analysis.