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Symbolic Algebraic Methods and Verification Methods

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ISBN-10: 3211835938

ISBN-13: 9783211835937

Edition: 2001

Authors: G�tz Alefeld, Jiri Rohn, Siegfried M. Rump, Tetsuro Yamamoto

List price: $129.00
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The usual implementation of real numbers as floating point numbers on existing computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. During the last years research in different areas has been intensified in order to overcome these problems. (LEDA-Library by K. Mehlhorn et al., Exact arithmetic with real numbers by A. Edalat et al., Symbolic algebraic methods, verification methods). The latest development is the combination of symbolic-algebraic methods and verification methods to so-called hybrid methods. This book contains a collection of…    
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Book details

List price: $129.00
Copyright year: 2001
Publisher: Springer
Publication date: 2/12/2001
Binding: Paperback
Pages: 266
Size: 6.69" wide x 9.61" long x 0.50" tall
Weight: 1.210
Language: English

List of Contributors
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 Results 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 Subdivision in Multi-dimensional Verified Gaussian Quadrature
On the Shape, of the Fixed Points of [f]([x]) = [A][x] + [b]
Exact Computation with ledareal - Theory and Geometric 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 Dirichlet Problems
How Orthogonality is Lost in Krylov Methods