Validation numerics : theory and applications ; [this volume is dedicated to Professor Dr. Ulrich Kulisch ... on the occasion of his 60th birthday

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. Front Matter....Pages i-ix On a Unified Concept of Mathematics....Pages 1-10 A General Approach to a Class of Single-Step Methods for the Simultaneous Inclusion of Polynomial Zeros....Pages 11-19 On Some Properties of an Interval Newton Type Method and its Modification....Pages 21-32 Verified Solution of the Integral Equations for the Two-Dimensional Dirichlet and Neumann Problem....Pages 33-43 Two-Stage Interval Iterative Methods....Pages 45-65 Convergence Acceleration for Some Rootfinding Methods....Pages 67-78 A Program for Enclosing Cumulative Binomial Probabilities....Pages 79-92 Effective Evaluation of Hausdorff Distances for Finite Unions of Hyperrectangles....Pages 93-100 A Verified Computation of Fourier-Representations of Solutions for Functional Equations....Pages 101-115 The Cluster Problem in Global Optimization: the Univariate Case....Pages 117-127 Developing Expert Systems for Validating Numerics....Pages 129-146 Computation of Interval Bounds for Weierstrass’ Elliptic Function ℘( z )....Pages 147-159 Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration....Pages 161-173 The Wrapping Effect, Ellipsoid Arithmetic, Stability and Confidence Regions....Pages 175-190 Validated Solution of Large Linear Systems....Pages 191-212 The Interval Buneman Algorithm for Arbitrary Block Dimension....Pages 213-231 On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations....Pages 233-246 Verification in Computer Algebra Systems....Pages 247-263 FORTRAN-XSC A Portable Fortran 90 Module Library for Accurate and Reliable Scientific Computing....Pages 265-285 Implementation of Accurate Matrix Multiplication on the CM-2....Pages 287-291