Günter Mayer
On a Unified Representation of Some Interval Analytic Algorithms
The paper is published: Rostocker Mathematische Kolloquium, Rostock. Math. Kolloq. 49, 75-88 (1995)
65F15 Eigenvalues, eigenvectors
65G10 Interval and finite arithmetic
Abstract: In this article we show that several interval analytic algorithms for
verifying solutions $ x^* $ of various mathematical problems can be viewed
as special cases of some iterative method involving the first and the
second derivative of the underlying function. Starting with an
approximation of $ x^* $ a way is given how to construct interval vectors
which contain $ x^* $, and how to improve these interval bounds.

Keywords: Systems of nonlinear equations, second order methods, enclosure methods, verification methods, interval methods for nonlinear systems, algebraic eigenproblem, singular value decomposition, quadratic systems, invariant supspaces