Validation Numerics

The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

Contenu

On a Unified Concept of Mathematics.- A General Approach to a Class of Single-Step Methods for the Simultaneous Inclusion of Polynomial Zeros.- On Some Properties of an Interval Newton Type Method and its Modification.- Verified Solution of the Integral Equations for the Two-Dimensional Dirichlet and Neumann Problem.- Two-Stage Interval Iterative Methods.- Convergence Acceleration for Some Rootfinding Methods.- A Program for Enclosing Cumulative Binomial Probabilities.- Effective Evaluation of Hausdorff Distances for Finite Unions of Hyperrectangles.- A Verified Computation of Fourier-Representations of Solutions for Functional Equations.- The Cluster Problem in Global Optimization: The Univariate Case.- Developing Expert Systems for Validating Numerics.- Computation of Interval Bounds for Weierstrass' Elliptic Function ? (z).- Solving Nonlinear Elliptic Problems with Result Verification Using an H-1 Type Residual Iteration.- The Wrapping Effect, Ellipsoid Arithmetic, Stability and Confidence Regions.- Validated Solution of Large Linear Systems.- The Interval Buneman Algorithm for Arbitrary Block Dimension.- On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations.- Verification in Computer Algebra Systems.- FORTRAN-XSC. A Portable Fortran 90 Module Library for Accurate and Reliable Scientific Computing.- Implementation of Accurate Matrix Multiplication on the CM-2.