Article
MSC:
65F05,
65F10,
65F15,
65G05,
65G10,
65G50,
65H10,
65H15,
65L05 | MR 1627997 | Zbl 0938.65058 | DOI: 10.1023/A:1023297204431
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Keywords:
epsilon-inflation; P-contraction; contraction; verification algorithms; interval computation; nonlinear equations; eigenvalues; singular values
epsilon-inflation; P-contraction; contraction; verification algorithms; interval computation; nonlinear equations; eigenvalues; singular values
Summary:
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.
References:
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