## On the convergence of some interval-arithmetic modifications of Newton’s method.(English)Zbl 0536.65026

This interesting paper studies an interval version of Newton’s method for solving systems of n nonlinear equations, in which the auxiliary linear interval equation is solved by Gauss elimination. Main result: The method converges (or shows no existence of a solution) if the spectral radius of the matrix $$| I-IGA({\mathcal A})\cdot {\mathcal A}|$$ is less than one, where $${\mathcal A}=f'(x^ 0)$$ and IG$$A({\mathcal A})$$ is the inverse of $${\mathcal A}$$ computed by applying Gauss elimination to the columns of $${\mathcal A}$$. Unfortunately the test is unpractical for band matrices, requiring e.g. $$O(n^ 2)$$ operations for tridiagonal $${\mathcal A}$$.
Reviewer: A.Neumaier

### MSC:

 65H10 Numerical computation of solutions to systems of equations 65G30 Interval and finite arithmetic
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