Validation Numerics: Theory and Applications

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