Geodesic
Epsilon-inflation with contractive interval functions
Applications of Mathematics, Tome 43 (1998) no. 4, pp. 241-254.

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For contractive interval functions $ [g] $ we show that $ [g]([x]^{k_0}_\epsilon ) \subseteq \int ([x]^{k_0}_\epsilon ) $ results from the iterative process $ [x]^{k+1} := [g]([x]^k_\epsilon ) $ after finitely many iterations if one uses the epsilon-inflated vector $ [x]^k_\epsilon $ as input for $ [g] $ instead of the original output vector $ [x]^k $. Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.
DOI : 10.1023/A:1023297204431
Classification : 65F05, 65F10, 65F15, 65G05, 65G10, 65G50, 65H10, 65H15, 65L05
Keywords: epsilon-inflation; P-contraction; contraction; verification algorithms; interval computation; nonlinear equations; eigenvalues; singular values 
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     title = {Epsilon-inflation with contractive interval functions},
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Mayer, Günter. Epsilon-inflation with contractive interval functions. Applications of Mathematics, Tome 43 (1998) no. 4, pp. 241-254. doi : 10.1023/A:1023297204431. http://geodesic.mathdoc.fr/articles/10.1023/A:1023297204431/

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