Ebook: Inclusion Methods for Nonlinear Problems: With Applications in Engineering, Economics and Physics

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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The book covers recent 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. The bulk of the presented algorithms deal with problems from various fields in the applied sciences.

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The book covers recent 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. The bulk of the presented algorithms deal with problems from various fields in the applied sciences.
Content:
Front Matter....Pages I-XII
On Symmetric Solution Sets....Pages 1-22
Methods for Computing All Roots of a Polynomial Simultaneously ­ Known Results and Open Problems....Pages 23-35
Narrow Bounds for the Effective Rate of Return Concerning a Special Problem for Annuities....Pages 37-43
Algorithmic Differentiation with Intervals....Pages 45-65
Computation of a Family of Non-cosymmetrical Equilibria in a System of Nonlinear Parabolic Equations....Pages 67-82
Quadratic Convergence of Scaled Iterates by Kogbetliantz Method....Pages 83-105
On a Method for Computing Inclusions of Solutions of the Basic GPS Equations....Pages 107-119
Construction of Bounds for the Positive Root of a General Class of Polynomials with Applications....Pages 121-133
Rounding Near Zero....Pages 135-142
a Note on the Convergence of the SOR-like Weierstrass Method....Pages 143-149
Boundary Regularity Aspects in Solving Contact Problems....Pages 151-163
Convex-decomposable Operators and Inclusive Algorithms....Pages 165-170
Fast Inclusion and Residual Iteration for Solutions of Matrix Equations....Pages 171-184
Schr?der-like Methods for the Simultaneous Inclusion of Polynomial Zeros....Pages 185-197
Interval Root-finding Methods of Laguerre’s Type*....Pages 199-211
Exact Behavior of Singularities of Protter’s Problem for the 3-D Wave Equation....Pages 213-236
Construction of Shortest Line of Restricted Curvature in a Non-singly-connected Polygonal Area....Pages 237-244
Back Matter....Pages 245-251

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The book covers recent 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. The bulk of the presented algorithms deal with problems from various fields in the applied sciences.
Content:
Front Matter....Pages I-XII
On Symmetric Solution Sets....Pages 1-22
Methods for Computing All Roots of a Polynomial Simultaneously ­ Known Results and Open Problems....Pages 23-35
Narrow Bounds for the Effective Rate of Return Concerning a Special Problem for Annuities....Pages 37-43
Algorithmic Differentiation with Intervals....Pages 45-65
Computation of a Family of Non-cosymmetrical Equilibria in a System of Nonlinear Parabolic Equations....Pages 67-82
Quadratic Convergence of Scaled Iterates by Kogbetliantz Method....Pages 83-105
On a Method for Computing Inclusions of Solutions of the Basic GPS Equations....Pages 107-119
Construction of Bounds for the Positive Root of a General Class of Polynomials with Applications....Pages 121-133
Rounding Near Zero....Pages 135-142
a Note on the Convergence of the SOR-like Weierstrass Method....Pages 143-149
Boundary Regularity Aspects in Solving Contact Problems....Pages 151-163
Convex-decomposable Operators and Inclusive Algorithms....Pages 165-170
Fast Inclusion and Residual Iteration for Solutions of Matrix Equations....Pages 171-184
Schr?der-like Methods for the Simultaneous Inclusion of Polynomial Zeros....Pages 185-197
Interval Root-finding Methods of Laguerre’s Type*....Pages 199-211
Exact Behavior of Singularities of Protter’s Problem for the 3-D Wave Equation....Pages 213-236
Construction of Shortest Line of Restricted Curvature in a Non-singly-connected Polygonal Area....Pages 237-244
Back Matter....Pages 245-251
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