## Scientific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN-95 Held in Wuppertal, Germany, September 26-29, 1995The International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN is held biannually, the fourth conference took place in Wuppertal 1995. This volume contains contributions from outstanding research specialists based on their presentations at SCAN–95. It covers all aspects of scientific computing with validation, starting with the latest developments in the design of floating point units together with algorithms for floating point operations and elementary function evaluations with maximum accuracy. The book continues by treating scientific computing methods for many areas of applied mathematics such as numerical linear algebra, nonlinear equations, global optimization, ordinary and partial differential equations and dynamical systems. Some computer science aspects like complexity are also considered as are examples where validation methods have successfully be used in applications from the engineering sciences. |

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### Contents

Hardware and Floating Point Operations | 11 |

A Processor for Accurate SelfValidating Computing | 25 |

Function Evaluation | 38 |

Copyright | |

20 other sections not shown

### Common terms and phrases

accuracy Alefeld algebraic algorithm applied approximation arithmetic operations arithmetic-geometric mean assume assumptions automatic differentiation bifurcation bisection bisection method bits calculate Cauchy principal value coefficients complex Computer Arithmetic consider convergence defined denote derivatives digits division eigenvalue elementary functions elements enclosure endpoints equations error estimate evaluation example existence finite floating point floating-point formula Gauss-Seidel method given global optimization hardware Herzberger IEEE implementation inclusion input instructions interval analysis interval arithmetic Interval Computations interval Newton method interval vector iteration Kaucher Kulisch Lemma lower bound machine number mantissa Math Mathematics matrix multiplier nonlinear NP-hard NULL obtained operand optimal solution parallel Pascal-XSC performed polynomial precision preconditioner processor programming real numbers reciprocal table representation rounding mode Scientific Computing significand simulation software metrics solution branch solution set solve square root strategy subboxes subdefinite subproblem techniques Theorem upper bounds valid variable-precision interval variables verified zero