**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)

**MSC:**- 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 *