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Decomposition methods: A new proof of convergence. (English) Zbl 0805.65057
The authors consider nonlinear equations of the form (*) $$u-N(u)=f$$ where $$N$$ and $$f$$, respectively, are operator and function given in convenient spaces. They construct a solution of (*) in the form (+) $$u=\sum^ \infty_{i=0} u_ i$$ where the $$u_ i$$ are successively defined. A convergence proof of the series (+) is proposed and the error of the truncated series of (+) is estimated. No application is given.
[Remark: The proof is not very distinct; in particular, the space in which the proof is valid is not stated].

##### MSC:
 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators
##### Keywords:
nonlinear operator equation; error estimate; convergence
Full Text:
##### References:
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