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Epsilon-inflation with contractive interval functions |
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| Authors: | Günter Mayer |
| Affiliation: | (1) Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, D-18051 Rostock, Germany |
| Abstract: | For contractive interval functions [g] we show that  subseteq operatorname{int} ([x]_varepsilon ^{k_0 } )$$](/content/w126108m0664q320/10492_2004_Article_420333_TeX2GIFIE1.gif) results from the iterative process ![$$[x]^{k + 1} : = [g]([x]_varepsilon ^k )$$](/content/w126108m0664q320/10492_2004_Article_420333_TeX2GIFIE2.gif) after finitely many iterations if one uses the epsilon-inflated vector ![$$[x]_varepsilon ^k$$](/content/w126108m0664q320/10492_2004_Article_420333_TeX2GIFIE3.gif) 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. |
| Keywords: | epsilon-inflation P-contraction contraction verification algorithms interval computation nonlinear equations eigenvalues singular values |
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