## Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis): (Computer-Orientated Numerical Analysis)This volume contains mainly a collection of the invited lectures which were given during a conference on "Fundamentals of Numerical Computation", held in June, 5 - 8, 1979, on the occasion of the centennial of the Technical University of Berlin. About hundred scientists from several countries attended this conference. A preceding meeting on "Fundamentals of Computer-Arithmetic" was held in August, 1975, at the "Mathematisches Forschungsinstitut Oberwolfach". The lectures of this conference have been published as Supplementum 1 of Computing (Editors R. Albrecht, U. Kulisch). After a period of four years of active research the purpose of the Berlin-Conference was to give a broad survey of the present status of the closely connected topics Interval Analysis, Mathematical Foundation of Computer Arithmetic, Rounding Error Analysis and Stability of Numerical Algorithms and to give prospects of future activities in these fields. Besides the invited lectures 35 short com munications, each of 20 minutes length, were given. We gratefully acknowledge the support of the President of the Technical University and of his Aussenreferat as well as of the Department of Mathematics. Besides these institutions financial support was given by AEG-Telefunken, Berlin, Allianz Lebensversicherungs A.G., Stuttgart, CDC, Hamburg/Berlin, DAT A 100, Munchen, Gesellschaft von Freunden der TU Berlin e.V., Berlin and Siemens AG., Berlin. Finally we express our thanks to Mrs. G. Froehlich and Mrs. B. Trajanovic, who managed the paper work before, during and after the conference. |

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### Contents

On Methods for the Construction of the Boundaries of Sets | 1 |

Roundings and Approximations in Ordered Sets | 17 |

Interval Analysis in the Extended Interval Space OR | 33 |

Copyright | |

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### Other editions - View all

Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis) R Albrecht,U Kulisch,F Stummel No preview available - 1980 |

### Common terms and phrases

7adh accuracy adjacent fractions algebraic algorithm antitone applications approximation arithmetic operations AUGMENT precompiler automatic differentiation BPA numbers Brent package co-adh coefficients computation continued fractions convergence data type defined definition denote digits directed rounding double precision endpoint error analysis error bounds error estimates evaluation finite precision fixed-slash and floating-slash floating point floating-point floating-point numbers formulas FORTRAN fraction number systems graph implementation integer interval analysis interval arithmetic package interval function interval mathematics interval package irreducible fractions isomorphism isotone iterative methods Karlsruhe linear mapping Math Mathematics Research Center matrix Matula monotone Moore multiple precision arithmetic numerical analysis obtain partial sums polynomial precision arithmetic priori condition numbers priori error Proof properties real numbers recursion relative a priori relative error representable values resp respect rounding error routine safe starting region satisfied semimorphism sequence simple chain spaces summation Theorem united extension variable vector Wisconsin-Madison