(Q26926645)

English

convergent numerical method

numerical method in which the approximations of the resolvent on perturbed data are abritrary close to the resolvent on the exact data

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{\begin{aligned}\forall \varepsilon >0,\exists n_{0}\in \mathbb {N} ,\exists \delta _{n_{0},\varepsilon }>0{\text{ such that }}\\\forall n>n_{0},\forall l_{n}:\lVert l_{n}\rVert <\delta _{n_{0},\varepsilon }\\\Rightarrow \lVert g(x)-g_{n}(x+l_{n})\rVert <\varepsilon \end{aligned}}

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\lim g_{n}=g\Rightarrow \left\{F_{n}(x_{n},g_{n}(x_{n}))=0\right\}_{n\in \mathbb {N} }{\text{ is convergent}}

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