Scientific Computing, Validated Numerics, Interval Methods

The papers in this book discuss a wide variety of serious applications of all parts of mathematical modelling. New efficient, publicly available or even commercial tools are proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened. They are concerned not only with applications of well known enclosure methods or the development of new-self validating algorithms, but also transfer the mechanisms and design process known from these areas to other fields. The 31 contributions to this proceedings volume were carefully selected from a much larger number of submissions.

SCAN 2000 Keynote Address The Future of Intervals -- I Software- and Hardware-Tools -- Variable-Precision Exponential Evaluation -- Fast computation of some special integrals of mathematical physics -- Interval Input and Output -- A Case for Interval Hardware on Superscalar Processors -- Evaluating the Impact of Accurate Branch Prediction on Interval Software -- Automatic Test Case Generation using Interval Arithmetic -- II Linear Algebra -- On the Hull of the Solution Sets of Interval Linear Equations -- Computation of Algebraic Solutions to Interval Systems via Systems of Coordinates -- Towards Diagrammatic Analysis of Systems of Interval "Linear Equations" -- On the Solution of Parametrised Linear Systems -- III Polynomials -- Verified solutions of systems of nonlinear polynomial equations -- Euler-like method with Weierstrass' correction -- IV Set Enclosures -- Guaranteed Set Computation with Subpavings -- A New Intersection Algorithm for Parametric Surfaces Based on LIEs -- State estimation using interval constraint propagation -- V Global Optimization -- Interval Methods for Global Optimization Using the Boxing Method -- A Branch-and-Prune Method for Global Optimization -- S…