Esistenza,unicità e calcolo della soluzione di un sistema non lineare |
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Authors: | O G Mancino |
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Affiliation: | 1. Istituto di Elaborazione della Informazione del C. N. R., Pisa
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Abstract: | LetX be a point of the realn-dimensional Euclidean space ? n ,G(X) a given vector withn real components defined in ? u ,U an unknown vector withs real components,K a known vector withs real components andA a given reals×n matrix of ranks. Assuming that, for every pair of pointsX 1 , X2of ? n ,G(X) satisfies the conditions $$(G(X_1 ) - G(X_2 ), X_1 - X_2 ) \geqslant o (X_1 - X_2 , X_1 - X_2 )$$ and $$\left\| {(G(X_1 ) - G(X_2 )\left\| { \leqslant M} \right\|X_1 - X_2 )} \right\|$$ wherec andM are positive constants, we prove that a unique solution of the system $$\left\{ \begin{gathered} G(X) + A ^T U = 0 \hfill \\ AX = K \hfill \\ \end{gathered} \right.$$ exists and we show a method for finding such a solution |
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