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Epsilon-inflation with contractive interval functions

Günter Mayer — 1998

Applications of Mathematics

For contractive interval functions [ g ] we show that [ g ] ( [ x ] ϵ k 0 ) ( [ x ] ϵ k 0 ) results from the iterative process [ x ] k + 1 : = [ g ] ( [ x ] ϵ k ) after finitely many iterations if one uses the epsilon-inflated vector [ x ] ϵ k 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.

A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices

Günter MayerLars Pieper — 1993

Applications of Mathematics

A necessary and sufficient to guarantee feasibility of the interval Gaussian algorithms for a class of matrices. We apply the interval Gaussian algorithm to an n × n interval matrix [ A ] the comparison matrix [ A ] of which is irreducible and diagonally dominant. We derive a new necessary and sufficient criterion for the feasibility of this method extending a recently given sufficient criterion.

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