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

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### Contents

Interval Acceleration of Convergence | 151 |

Solving Systems of Lineor Interval Equations 474 | 171 |

Existence of Solutions ond Iterotions for Nonlinedr Equotions | 204 |

Copyright | |

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### Common terms and phrases

accuracy addition algorithm analysis applied approach approximation array assumed bounds called carry coefficients column complex components computed consider contain continuous convergence corresponding defined denotes derivatives determine developed differentiation digits discuss dynamic equations error estimates evaluation example exists exponent expressions extension Figure floating-point FORTRAN FORTRAN-SC function given gives global holds implementation inclusion integer interval arithmetic introduced iteration known least length linear system machine mapping Mathematics matrix means method nonlinear Note observations obtained operations optimization parameter polynomials positive possible precision Press problem procedure properties range References respectively result rounding scalar sequence shown shows simple single solution solving space standard step summands summing Taylor Theorem theory tion University variables vector width write zero