Perspectives on Enclosure Methods
By: edited by Ulrich Kulisch, Rudolf Lohner, Axel Facius
Contributors: Lohner, Rudolf; Facius, Axel
Publisher: Springer Vienna; Imprint; Springer
Published: 2001
Place of publication: Vienna
Language: eng
Format: [electronic resource] /
Number of pages: 345
ISBN-13: 9783709162828
Description: Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.
Table of contents: title: Proving Conjectures by Use of Interval Arithmetic (Andreas Frommer); title: Advanced Arithmetic for the Digital Computer Interval Arithmetic Revisited (Ulrich W. Kulisch); title: Highly Accurate Verified Error Bounds for Krylov Type Linear System Solvers (Axel Facius); title: Elements of Scientific Computing (J. Hartmut Bleher); title: The Mainstreaming of Interval Arithmetic (John L. Gustafson); title: Bounds for Eigenvalues with the Use of Finite Elements (Henning Behnke, Ulrich Mertins); title: Algorithmic Differencing (Louis B. Rall, Thomas W. Reps); title: A Comparison of Techniques for Evaluating Centered Forms (Bruno Lang); title: On the Limit of the Total Step Method in Interval Analysis (Günter Mayer, Ingo Warnke); title: How Fast can Moore's Interval Integration Method Really be? (Jürgen Herzberger); title: Numerical Verification and Validation of Kinematics and Dynamical Models for Flexible Robots in Complex Environments (Wolfram Luther, Eva Dyllong, Daniela Fausten, Werner Otten, Holger Traczinski); title: On the Ubiquity of the Wrapping Effect in the Computation of Error Bounds (Rudolf J. Lohner); title: A New Perspective on the Wrapping Effect in Interval Methods for Initial Value Problems for Ordinary Differential Equations (Nedialko S. Nedialkov, Kenneth R. Jackson); title: A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Elements (Mitsuhiro T. Nakao, Nobito Yamamoto); title: Nonsmooth Global Optimization (Dietmar Ratz).