## Inclusion Methods for Nonlinear Problems: With Applications in Engineering, Economics and PhysicsThis workshop was organized with the support of GAMM, the International Association of Applied Mathematics and Mechanics, on the occasion of J. Herzberger's 60th birthday. GAMM is thankful to him for all the time and work he spent in the preparation and holding of the meeting. The talks presented during the workshop and the papers published in this volume are part of the field of Verification Numerics. The important subject is fostered by GAMM already since a number of years, especially also by the GAMM FachausschuB (special interest group) "Rechnerarithmetik und Wissenschaft liches Rechnen". GiHz Alefeld Karlsruhe, Dezember 2001 (President of GAMM) Preface At the end of the year 2000, about 23 scientists from many countries gathered in the beautiful city of Munich on the occasion of the International GAMM Workshop on "Inclusion Methods for Nonlinear Problems with Applications in Engineering, Economics and Physics" from December 15 to 18. The purpose of this meeting was to bring together representatives of research groups from Austria, Bulgaria, China, Croatia, Germany, Japan, Russia, Ukraine and Yugoslavia who in a wider sense work in the field of calculating numerical solutions with error-bounds. Most of those participants have already known each other from earlier occasions or closely cooperated in the past. Representatives from three Academies of Sciences were among the speakers of this conference: from the Bulgarian Academy, the Russian Academy and the Ukrainian Academy of Sciences. |

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### Contents

On Symmetric Solution Sets G Alefeld V Kreinovich and G Mayer | 1 |

Methods for Computing All Roots of a Polynomial Simultaneously Known Results and Open Problems | 23 |

References | 43 |

Algorithmic Differentiation with Intervals | 45 |

Computation of a Family of Noncosymmetrical Equilibria in a System of Nonlinear Parabolic Equations | 67 |

Quadratic Convergence of Scaled Iterates by Kogbetliantz Method | 83 |

On a Method for Computing Inclusions of Solutions of the Basic GPS Equations | 107 |

Construction of Bounds for the Positive Root of a General Class of Polynomials with Applications | 121 |

A Note on the Convergence of the SORlike Weierstrass Method | 143 |

Boundary Regularity Aspects in Solving Contact Problems | 151 |

Convexdecomposable Operators and Inclusive Algorithms | 165 |

Fast Inclusion and Residual Iteration for Solutions of Matrix Equations | 171 |

Schroderlike Methods for the Simultaneous Inclusion of Polynomial Zeros | 185 |

Interval Rootfinding Methods of Laguerres Type | 199 |

Exact Behavior of Singularities of Protters Problem for the 3D Wave Equation | 213 |

Construction of Shortest Line of Restricted Curvature in a Nonsinglyconnected Polygonal Area | 237 |

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Inclusion Methods for Nonlinear Problems: With Applications in Engineering ... Jürgen Herzberger No preview available - 2003 |

### Common terms and phrases

5sym additive inverse Alefeld algebraic algorithm algorithm FUN annuity applied arithmetic assume boundary conditions boundary value problem calculating centered inversion clothoid coefficients complex consider contact zone cosymmetry defined denote derivatives diagonal double precision elements error bound estimate family of equilibria floating-point formula function given Herzberger high precision computation holds inclusion disks inclusion methods inequalities interval interval arithmetic iterative methods Jacobi method Kogbetliantz method Kyurkchiev Lemma linear lower bound Math Mathematics Mathematics Subject Classification matrix monotone Newton's Newton's method nonlinear obtained order of convergence paper parameters Petkovic polynomial equation polynomial zeros positive root Printed in Austria Problem PI proof of 18 quadruple precision R-order radii relation residual iteration reverse mode satisfies Schroder's Sect simultaneous inclusion singular values solution set solving Ssym step stick zone symmetric Theorem 5.1 unique additive inverse upper bound vector Weierstrass Weierstrass method