Symbolic Algebraic Methods and Verification Methods

Table of Contents

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   Book Overview
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   Chapter 1 Introduction
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   Chapter 2 Topological Concepts for Hierarchies of Variables, Types and Controls
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   Chapter 3 Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem
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   Chapter 4 Symbolic-Numeric Algorithms for Polynomials: some recent results
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   Chapter 5 Symbolic-Numeric QD-algorithms with applications in Function theory and Linear algebra
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   Chapter 6 Isoefficiency and the Parallel Descartes Method
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   Chapter 7 Matrix Methods for Solving Algebraic Systems
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   Chapter 8 A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure
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    Chapter 9 Solution of Systems of Polynomial Equations by Using Bernstein Expansion
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    Chapter 10 Symbolic-Algebraic Computations in a Modeling Language for Mathematical Programming
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    Chapter 11 Translation of Taylor series into LFT expansions
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    Chapter 12 Quasi Convex-Concave Extensions
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    Chapter 13 Rewriting, Induction and Decision Procedures: A Case Study of Presburger Arithmetic
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    Chapter 14 Derivative-Based Subdivision in Multi-Dimensional Verified Gaussian Quadrature
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    Chapter 15 On the Shape of the Fixed Points of [f]([x]) = [A] [x] + [b]
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    Chapter 16 Exact Computation with leda_real — Theory and Geometrie Applications
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    Chapter 17 Numerical Verification Method for Solutions of Nonlinear Hyperbolic Equations
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    Chapter 18 Geometric Series Bounds for the Local Errors of Taylor Methods for Linear n -th Order ODEs
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    Chapter 19 Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems
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    Chapter 20 Fast verification algorithms in Matlab
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    Chapter 21 The Linear Complementarity Problem with Interval Data
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    Chapter 22 Some Numerical Methods for Nonlinear Least Squares Problems
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    Chapter 23 A New Insight of the Shortley-Weller Approximation for Dirichlet Problems
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    Chapter 24 How Orthogonality is Lost in Krylov Methods