Symbolic Algebraic Methods and Verification Methods
By: edited by Götz Alefeld, Jiří Rohn, Siegfried Rump, Tetsuro Yamamoto
Contributors: Rohn, Jiří; Rump, Siegfried; Yamamoto, Tetsuro
Publisher: Springer Vienna; Imprint; Springer
Published: 2001
Place of publication: Vienna
Language: eng
Format: [electronic resource] /
Number of pages: 266
ISBN-13: 9783709162804
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 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.
Table of contents: title: Introduction (G. Alefeld, J. Rohn, S. Rump, T. Yamamoto); title: Topological Concepts for Hierarchies of Variables, Types and Controls (R. Albrecht); title: Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem (G. Alefeld, V. Kreinovich, G. Mayer); title: Symbolic-Numeric Algorithms for Polynomials: Some Recent Results (R. Corless); title: Symbolic-Numeric QD-Algorithms with Applications in Function Theory and Linear Algebra (A. Cuyt); title: On the Isoefficiency of the Parallel Descartes Method (Th. Decker, W. Krandick); title: Matrix Methods for Solving Algebraic Systems (I.Z. Emiris); title: A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure (A. Frommer); title: Solution of Systems of Polynomial Equations by Using Bernstein Expansion (J. Garloff, A.P. Smith); title: Symbolic-Algebraic Computations in Modeling Language for Mathematical Programming (D.M. Gay); title: Translation of Taylor Series into LFT Expansions (R. Heckmann); title: Quasi Convex-Concave Extensions (Chr. Jansson); title: Rewriting, Induction and Decision Procedures: A Case Study of Presburger Arithmetic (D. Kapur); title: Derivative-Based Subdivision in Multi-dimensional Verified Gaussian Quadrature (B. Lang); title: On the Shape of the Fixed Points of [f]([x]) = [A][x] + [b] (G. Mayer, I. Warnke); title: Exact Computation with leda_real; title: Theory and Geometric Applications (K. Mehlhorn, St. Schirra); title: Numerical Verification Method for Solutions of Nonlinear Hyperbolic Equations (T. Minamoto); title: Geometric Series Bounds for the Local Errors of Taylor Methods for Linear n-th-Order ODEs (M. Neher); title: Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems (M. Plum); title: Fast Verification Algorithms in MATLAB (S. Rump); title: The Linear Complementarity Problem with Interval Data (U. Schäfer); title: Some Numerical Methods for Nonlinear Least Squares Problems (St. Shakhno); title: A New Insight of the Shortley-Weller Approximation for Dirichlet Problems (T. Yamamoto); title: How Orthogonality is Lost in Krylov Methods (J. Zemke).