Inclusion Methods for Nonlinear Problems

With Applications in Engineering, Economics and Physics
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Jürgen Herzberger
460 g
244x170x14 mm

Covers developments in the construction and the analysis of numerical algorithms for the solution of nonlinear problems with emphasis on the automatic calculation of guaranteed errorbounds by machine interval operations.
On Symmetric Solution Sets.- Methods for Computing all Roots of a Polynomial Simultaneously - Known Results and Open Problems.- Narrow Bounds for the Effective Rate of Return Concerning a Special Problem for Annuities.- Algorithmic Differentiation with Intervals.- Computation of a Family of Noncosymmetrical Equilibria in a System of Nonlinear Parabolic Equations..- Quadratic Convergence of Scaled Iterates by Kogbetliantz Method.- On a Method for Computing Inclusions of Solutions of the Basic GPS Equations.- Construction of Bounds for the Positive Root of a General Class of Polynomials with Applications.- Rounding Near Zero.- A Note on the Convergence of the SOR-like Weierstrass Method.- Boundary Regularity Aspects in Solving Contact Problems.- The Convex-decomposable Operator and Inclusive Algorithm.- Fast Inclusion and Residual Iteration for Solutions of Matrix Equations.- Schroder-like Methods for the Simultaneous Inclusion of Polynomial Zeros.- Interval Root-finding Methods of Laguerre's Type.- Exact Behaviour of Singularities of Protter's Problem for the 3-D Wave Equation.- Construction of Shortest Line of Restricted Curvature in a Non-singly-connected Polygonal Area.
This 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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