Advanced Search

For contractive interval functions $\left[g\right]$ we show that $\left[g\right]\left({\left[x\right]}_{ϵ}^{k_0}\right)\subseteq \int \left({\left[x\right]}_{ϵ}^{k_0}\right)$ results from the iterative process ${\left[x\right]}^{k+1}:=\left[g\right]\left({\left[x\right]}_{ϵ}^k\right)$ after finitely many iterations if one uses the epsilon-inflated vector ${\left[x\right]}_{ϵ}^k$ as input for $\left[g\right]$ instead of the original output vector ${\left[x\right]}^k$. Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

We present a class of Newton-like methods to enclose solutions of systems of nonlinear equations. Theorems are derived concerning the feasibility of the method, its global convergence, its speed and the quality of enclosure.

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 $n\times n$ interval matrix $\left[A\right]$ the comparison matrix $〈\left[A\right]〉$ 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.