## Reliability in computing: the role of interval methods in scientific computing |

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### Contents

Arithmetic for Vector Processors 3 | 41 |

FORTRANSC A FORTRAN Extension for EngineeringScientific | 63 |

Reliable Expression Evaluation in PASCALSC | 81 |

Copyright | |

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Academic Press accuracy ACRITH adders algebraic applied approximation binary binary standard bounds Brouwer fixed-point theorem coefficients column complex interval components contain convergence corresponding data types decimal defined denotes derivatives differentiation arithmetic digits directed roundings dot product dot product expressions double precision dynamic arrays estimates evaluation example exists Figure finite floating-point arithmetic foldpoints FORTRAN FORTRAN-SC given global optimization Hurwitz IEEE implementation inclusion function input integer interval algorithms interval analysis interval arithmetic interval extension Interval Mathematics interval matrix interval methods interval Newton method interval vector inverse isotonic Karlsruhe Kulisch linear system manifold mapping Math Mathematics Miranker monotone Neumaier notation parameter PASCAL-SC quadrature real numbers result rounding modes scalar product Scientific Computation sequence SIAM single precision solution solving space summands summing matrix Taylor operators Taylor series Theorem tion ultra-arithmetic variables Weitek width zero