Symbolic Algebraic Methods and Verification Methods

Topological Concepts for Hierarchies of Variables, Types and Controls.- Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem.- Symbolic-Numeric Algorithms for Polynomials: Some Recent Results.- Symbolic-Numeric QD-Algorithms with Applications in Function Theory and Linear Algebra.- On the Isoefficiency of the Parallel Descartes Method.- Matrix Methods for Solving Algebraic Systems.- A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure.- Solution of Systems of Polynomial Equations by Using Bernstein Expansion.- Symbolic-Algebraic Computations in Modeling Language for Mathematical Programming.- Translation of Taylor Series into LFT Expansions.- Quasi Convex-Concave Extensions.- Rewriting, Induction and Decision Procedures: A Case Study of Presburger Arithmetic.- Derivative-Based Sub division in Multi-dimensional Verified Gaussian Quadrature.- On the Shape of the Fixed Points of [f]([x]) = [A][x] + [b].- Exact Computation with leda_real - Theory and Geometrie Applications.- Numerical Verification Method for Solutions of Nonlinear Hyperbolic Equations.- Geometric Series Bounds for the Local Errors of Taylor Methods for Linear n-th-Order ODEs.- Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems.- Fast Verification Algorithms in MATLAB.- The Linear Complementarity Problem with Interval Data.- Some Numerical Methods for Nonlinear Least Squares Problems.- A New Insight of the Shortley-Weller Approximation for Diriehlet Problems.- How Orthogonality is Lost in Krylov Methods.