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On a unified representation of some interval analytic algorithms. (English) Zbl 0861.65049
This paper deals with methods for solving a system of nonlinear equations, \(f(x)=0\). A general scheme is described for computing interval enclosures of solutions. Hereby first and second derivatives of \(f\) are employed. It is shown that the general scheme comprises several existing interval methods for problems such as the algebraic eigenproblem, the generalized algebraic eigenproblem, the singular value decomposition problem, and the invariant subspace problem.

65H10 Numerical computation of solutions to systems of equations
65G30 Interval and finite arithmetic
65F15 Numerical computation of eigenvalues and eigenvectors of matrices