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Titlebook: Scientific Computation with Automatic Result Verification; Ulrich Kulisch,Hans J. Stetter Conference proceedings 1988 Springer-Verlag/Wien

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书目名称Scientific Computation with Automatic Result Verification
编辑Ulrich Kulisch,Hans J. Stetter
视频video
丛书名称Computing Supplementa
图书封面Titlebook: Scientific Computation with Automatic Result Verification;  Ulrich Kulisch,Hans J. Stetter Conference proceedings 1988 Springer-Verlag/Wien
描述Scientific Computation with Result Verification has been a persevering research topic at the Institute for Applied Mathematics of Karlsruhe University for many years. A good number of meetings have been devoted to this area. The latest of these meetings was held from 30 September to 2 October, 1987, in Karlsruhe; it was co-sponsored by the GAMM Committee on "Computer Arithmetic and Scientific Computation". - - This volume combines edited versions of selected papers presented at this confer­ ence, including a few which were presented at a similar meeting one year earlier. The selection was made on the basis of relevance to the topic chosen for this volume. All papers are original contributions. In an appendix, we have supplied a short account of the Fortran-SC language which permits the programming of algorithms with result verification in a natural manner. The editors hope that the publication of this material as a Supplementum of Computing will further stimulate the interest of the scientific community in this important tool for Scientific Computation. In particular, we would like to make application scientists aware of its potential. The papers in the second chapter of this volum
出版日期Conference proceedings 1988
关键词FORTRAN; Mathematica; Natural; algorithms; computer; complexity
版次1
doihttps://doi.org/10.1007/978-3-7091-6957-5
isbn_softcover978-3-211-82063-6
isbn_ebook978-3-7091-6957-5Series ISSN 0344-8029
issn_series 0344-8029
copyrightSpringer-Verlag/Wien 1988
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Enclosing the Solutions of Systems of Linear Equations by Interval Iterative Processeso vary within given intervals. The methods are based on so-called .-splittings and contain many standard iterative processes. We derive results concerning the feasibility, the global convergence, the quality of enclosure and the speed of convergence.
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Inclusion of Eigenvalues of General Eigenvalue Problems for Matricese quotients and their generalization by Lehmann, in connection with interval arithmetic. Numerical examples illustrate the fact that bounds for multiple or clustered eigenvalues can be calculated as well.
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Verified Inclusion for Eigenvalues of Certain Difference and Differential Equationsundary condition at infinity can be treated. Using interval arithmetic and the exact scalar product very accurate inclusions can be obtained even for ill conditioned problems where classical methods fail.
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Evaluation of Arithmetic Expressions with Guaranteed High Accuracy this tool to develop an algorithm for the evaluation of rational expressions in several variables with high guaranteed accuracy. An extension for complex expressions, vectormatrix expressions and expressions with standard functions and interval arguments is also given.
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