An edition of Symbolic Algebraic Methods and Verification Methods (2001)

Symbolic Algebraic Methods and Verification Methods

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Cover of: Symbolic Algebraic Methods and Verification Methods by Götz Alefeld, Götz Alefeld
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Last edited by MARC Bot
July 7, 2019 | History
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An edition of Symbolic Algebraic Methods and Verification Methods (2001)

Symbolic Algebraic Methods and Verification Methods

by

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 worked out talks on these subjects given during a Dagstuhl seminar at the Forschungszentrum f.r Informatik, Schlo. Dagstuhl, Germany, presenting the state of the art.

Publish Date
Publisher
Springer Vienna, Imprint, Springer
Language
English
Pages
266

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Cover of: Symbolic Algebraic Methods and Verification Methods
Symbolic Algebraic Methods and Verification Methods
Sep 07, 2011, Springer
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Cover of: Symbolic Algebraic Methods and Verification Methods
Symbolic Algebraic Methods and Verification Methods
2001, Springer Vienna, Imprint, Springer
electronic resource / in English

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Book Details

Table of Contents

Introduction (G. Alefeld, J. Rohn, S. Rump, T. Yamamoto)
Topological Concepts for Hierarchies of Variables, Types and Controls (R. Albrecht)
Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem (G. Alefeld, V. Kreinovich, G. Mayer)
Symbolic-Numeric Algorithms for Polynomials: Some Recent Results (R. Corless)
Symbolic-Numeric QD-Algorithms with Applications in Function Theory and Linear Algebra (A. Cuyt)
On the Isoefficiency of the Parallel Descartes Method (Th. Decker, W. Krandick)
Matrix Methods for Solving Algebraic Systems (I.Z. Emiris)
A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure (A. Frommer)
Solution of Systems of Polynomial Equations by Using Bernstein Expansion (J. Garloff, A.P. Smith)
Symbolic-Algebraic Computations in Modeling Language for Mathematical Programming (D.M. Gay)
Translation of Taylor Series into LFT Expansions (R. Heckmann)
Quasi Convex-Concave Extensions (Chr. Jansson)
Rewriting, Induction and Decision Procedures: A Case Study of Presburger Arithmetic (D. Kapur)
Derivative-Based Subdivision in Multi-dimensional Verified Gaussian Quadrature (B. Lang)
On the Shape of the Fixed Points of [f]([x]) = [A][x] + [b] (G. Mayer, I. Warnke)
Exact Computation with leda_real
Theory and Geometric Applications (K. Mehlhorn, St. Schirra)
Numerical Verification Method for Solutions of Nonlinear Hyperbolic Equations (T. Minamoto)
Geometric Series Bounds for the Local Errors of Taylor Methods for Linear n-th-Order ODEs (M. Neher)
Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems (M. Plum)
Fast Verification Algorithms in MATLAB (S. Rump)
The Linear Complementarity Problem with Interval Data (U. Schäfer)
Some Numerical Methods for Nonlinear Least Squares Problems (St. Shakhno)
A New Insight of the Shortley-Weller Approximation for Dirichlet Problems (T. Yamamoto)
How Orthogonality is Lost in Krylov Methods (J. Zemke).

Edition Notes

Published in
Vienna

Classifications

Library of Congress
QA1-939

The Physical Object

Format
[electronic resource] /
Pagination
1 online resource (IX, 266 pages 40 illustrations)
Number of pages
266

Edition Identifiers

Open Library
OL27090390M
Internet Archive
symbolicalgebrai00alef
ISBN 10
3709162807
ISBN 13
9783709162804
OCLC/WorldCat
840302641

Work Identifiers

Work ID
OL19905229W

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Internet Archive item record
Better World Books record

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