## Einführung in Die IntervallrechnungThis book is revised and expanded version of the original German text. The arrangement of the material and the structure are essentially unchanged. All remarks in the Preface to the German Edition regarding naming conventions for formulas, theorems, lemmas, and definitions are still valid as are those concerning the arrangement and choice of material. |

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### Contents

Real Interval Arithmetic l | 1 |

Further Concepts and Properties | 10 |

Interval Evaluation and Range of Real Functions | 20 |

Copyright | |

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absolute value Alefeld ALGOL 60 analogous Angew Apostolatos applied approximation assume bilinear operators binary operation bounds calculated Chapter complete induction complex interval components Computing consider convergence Corollary def1ned Definition denoted diagonal eigenvalues einige Anwendungen elements example FOR'J function Furthermore Gaussian algorithm given Herzberger holds Horner scheme including intervals inclusion monotonicity inequality Interval Analysis interval evaluation interval matrix interval operations interval vector Intervallrechnung inverse iteration procedure Iterationsverfahren Karlsruhe Kulisch Lemma linear m(xm machine interval arithmetic manner mantissa Math Mathematik matrix norm Mech Newton's method nonlinear nonnegative nonnegative matrix nonsingular obtains parameter point matrix point vector polynomial proof properties prove R. E. Moore Ratschek real interval real numbers regula falsi relation resp result Rokne satisfies sequence single step method solution spectral radius SSIC statements system of equations total step method unique fixed point Univ valid Varga Vn(U width zero