## Numerical methods and error bounds: proceedings of the IMACS-GAMM International Symposium on Numerical Methods and Error Bounds held in Oldenburg, Germany, July 9-12, 1995This volume contains the invited talks and short communications presented at the IMACS-GAMM International Symposium. The participants from all over the world presented their results in the field of development and investigation of numerical algorithms under the aspect of constructing proper error bounds for approximated solutions. Among the subjects of the talks were problems like systems of linear and nonlinear equations,ordinary and partial differential equation solvers, data fitting methods, computer geometry, computer arithmetic, interval arithmetic, and selected problems in theoretical mechanics. |

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### Contents

Adzic | 15 |

Alefeld G | 22 |

Using special arithmetic in geometric algorithms | 38 |

Copyright | |

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accuracy Alefeld algebraic algorithm analytic function applied approximation arithmetic operations asynchronous Atanassova boundary Brent's method calculated coefficients complex components consider coprocessor defined definition denote differential equations digits enclosure error analysis error bounds error estimates evaluation exact error example exponent factorization floating point floating-point formula Germany given guaranteed Herzberger IEEE implementation inequalities initial integral interval arithmetic interval vector inverse quadratic interpolation iterative methods ITPACK Koenig theorem LAPACK Lemma linear system LINPACK mapping 17 Math Mathematics matrix nonlinear Numerical Methods obtained ODEs optimization order of convergence orthogonal parameters perturbation piecewise polynomial proof Q-order quadrature real numbers recursion right-hand side root rounding errors routines satisfy secant method sequence significand simple zeros simultaneous solution set solve SOR-like space spectral radius step subinterval summands symmetric Taylor series topological primitives two-sided valid value problems variable-precision verification VPIAC