## Topics in validated computations: proceedings of IMACS-GAMM International Workshop on Validated Computation, Oldenburg, Germany, 30 August-3 September 1993Mathematics of Computing -- Numerical Analysis. |

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### Contents

Basic definitions and properties of interval arithmetic J Herzberger | 1 |

Validated computation of polynomial zeros by the DurandKerner | 27 |

method T Yamamoto S Kanno and L Atanassova | 55 |

Copyright | |

8 other sections not shown

### Common terms and phrases

Alefeld algebraic algorithm Analysis Angew applied approximate solution assertion assume assumptions automatic differentiation boundary value problems branch and bound calculated components Computer Arithmetic condition consider contains convergence defined denote differential equations Durand-Kerner method eigenvalue problem eigenvectors Enclosure Methods error bounds evaluation example exists given global minimum point Global Optimization Hence Herzberger holds hyperpower hyperpower method implementation implies inclusion function inclusion methods inequality input data interval arithmetic interval matrix interval operations interval vector inverse inverse-positive iterative methods Kulisch Lemma linear programming linear programming problems linear systems Lohner lower bound Math Mathematics matrix multiplications matrix norm Mech Mnn(IR monotonicity multiplications nonlinear nonsingular norm NP-hard numerical obtain parameters Pascal-XSC polynomial positive definite Proof prove quadratic regular Rohn rounding errors S.M. Rump satisfied Scientific Computation Section sequence SIAM singular value solving step symmetric Theorem 2.1 unique Universitat upper bound verified width yields zero