## Reliability in Computing: The Role of Interval Methods in Scientific Computing |

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### Contents

Interval Accelerotion of Convergence | 154 |

Solving Systems of Lineor Intervol Equotions 474 | 171 |

Existence of Solutions ond ſterotions for Nonlinedr Equotions | 204 |

Copyright | |

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1988 by Academic Academic Press accuracy ACRITH adders algebraic algorithm applied approximation binary 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 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 vector isotonic iteration Karlsruhe Kulisch Let f linear system manifold mapping Math Mathematics monotone Moore Neumaier notation parameter PASCAL-SC polynomials procedure quadrature Rall RELIABILITY IN COMPUTING result rounding modes scalar product Scientific Computation sequence SIAM single precision solution solving space summands summing matrix Taylor series Theorem tion ultra-arithmetic variables Weitek width zero