Symbolic Algebraic Methods and Verification Methods

Name: Symbolic Algebraic Methods and Verification Methods
Price: 42.19 USD
Availability: InStock
ISBN: 9783211835937

ISBN-10: 3211835938

ISBN-13: 9783211835937

Edition: 2001

Authors: Gï¿½tz Alefeld, Jiri Rohn, Siegfried M. Rump, Tetsuro Yamamoto

List price: $129.00

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Description:

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…

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



Contents


List of Contributors


Introduction



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