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A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equations of the first kind

William J. KammererM. Zuhair Nashed — 1971

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Un metodo iterativo di G. Cimmino, relativo alle equazioni lineari algebriche, viene generalizzato ad una equazione integrale di prima specie: 𝔎 x = y . Ammettendo che il codominio R ( 𝔎 ) di 𝔎 abbia dimensione maggiore di uno, si prova che il metodo converge ad un unico vettore che rende minima la norma di 𝔎 x - y al variare di y nell'insieme R ( 𝔎 ) + R ( 𝔎 ) .

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