Validation Numerics

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.