Ebook: Scientific Computing, Validated Numerics, Interval Methods

Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.

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The papers in this book discuss a wide variety of serious applications of all parts of mathematical modelling. New efficient, publicly available or even commercial tools are proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened. They are concerned not only with applications of well known enclosure methods or the development of new-self validating algorithms, but also transfer the mechanisms and design process known from these areas to other fields. The 31 contributions to this proceedings volume were carefully selected from a much larger number of submissions.

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The papers in this book discuss a wide variety of serious applications of all parts of mathematical modelling. New efficient, publicly available or even commercial tools are proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened. They are concerned not only with applications of well known enclosure methods or the development of new-self validating algorithms, but also transfer the mechanisms and design process known from these areas to other fields. The 31 contributions to this proceedings volume were carefully selected from a much larger number of submissions.
Content:
Front Matter....Pages i-x
SCAN 2000 Keynote Address the Future of Intervals....Pages 1-15
Front Matter....Pages 17-17
Variable-Precision Exponential Evaluation....Pages 19-28
Fast Computation of Some Special Integrals of Mathematical Physics....Pages 29-40
Interval Input and Output....Pages 41-51
A Case for Interval Hardware on Superscalar Processors....Pages 53-68
Evaluating the Impact of Accurate Branch Prediction on Interval Software....Pages 69-79
Automatic Test Case Generation Using Interval Arithmetic....Pages 81-87
Front Matter....Pages 89-89
On the Hull of the Solution Sets of Interval Linear Equations....Pages 91-102
Computation of Algebraic Solutions to Interval Systems Via Systems of Coordinates....Pages 103-114
Towards Diagrammatic Analysis of Systems of Interval “Linear Equations”....Pages 115-126
On the Solution of Parametrised Linear Systems....Pages 127-138
Front Matter....Pages 139-139
Verified Solutions of Systems of Nonlinear Polynomial Equations....Pages 141-152
Euler-Like Method for the Simultaneous Inclusion of Polynomial Zeros with Weierstrass’ Correction....Pages 153-164
Front Matter....Pages 165-165
Guaranteed Set Computation with Subpavings....Pages 167-178
A New Intersection Algorithm for Parametric Surfaces Based on Linear Interval Estimations....Pages 179-190
Nonlinear State Estimation Using Forward-Backward Propagation of Intervals in an Algorithm....Pages 191-201
Front Matter....Pages 203-203
Interval Methods for Global Optimization Using the Boxing Method....Pages 205-213
A Branch-and-Prune Method for Global Optimization....Pages 215-226
Simulation of a Controlled Aircraft Elevator under Sensor Uncertainties....Pages 227-237
Front Matter....Pages 239-239
Traditional Parameter Estimation Versus Estimation of Guaranteed Parameter Sets....Pages 241-253
Front Matter....Pages 239-239
Stabilizing Control Design of Nonlinear Process Involving Uncertainties....Pages 255-265
Set Estimation, Computation of Volumes and Data Safety....Pages 267-278
Front Matter....Pages 279-279
Verified High-Order Integration of DAEs and Higher-Order ODEs....Pages 281-292
About a Finite Dimensional Reduction Method for Conservative Dynamical Systems and Its Applications....Pages 293-303
Verified Determination of Singularities in Chemical Processes....Pages 305-316
Modeling of Multibody Systems with Interval Arithmetic....Pages 317-327
Front Matter....Pages 329-329
On the algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic....Pages 331-341
Global Random Walk Simulations of Diffusion....Pages 343-354
Interval Computations as a Particular Case of a General Scheme Involving Classes of Probability Distributions....Pages 355-365
For Reliable and Powerful Scientific Computations....Pages 367-377
Reliable Representations of Strange Attractors....Pages 379-390
Back Matter....Pages 391-398

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The papers in this book discuss a wide variety of serious applications of all parts of mathematical modelling. New efficient, publicly available or even commercial tools are proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened. They are concerned not only with applications of well known enclosure methods or the development of new-self validating algorithms, but also transfer the mechanisms and design process known from these areas to other fields. The 31 contributions to this proceedings volume were carefully selected from a much larger number of submissions.
Content:
Front Matter....Pages i-x
SCAN 2000 Keynote Address the Future of Intervals....Pages 1-15
Front Matter....Pages 17-17
Variable-Precision Exponential Evaluation....Pages 19-28
Fast Computation of Some Special Integrals of Mathematical Physics....Pages 29-40
Interval Input and Output....Pages 41-51
A Case for Interval Hardware on Superscalar Processors....Pages 53-68
Evaluating the Impact of Accurate Branch Prediction on Interval Software....Pages 69-79
Automatic Test Case Generation Using Interval Arithmetic....Pages 81-87
Front Matter....Pages 89-89
On the Hull of the Solution Sets of Interval Linear Equations....Pages 91-102
Computation of Algebraic Solutions to Interval Systems Via Systems of Coordinates....Pages 103-114
Towards Diagrammatic Analysis of Systems of Interval “Linear Equations”....Pages 115-126
On the Solution of Parametrised Linear Systems....Pages 127-138
Front Matter....Pages 139-139
Verified Solutions of Systems of Nonlinear Polynomial Equations....Pages 141-152
Euler-Like Method for the Simultaneous Inclusion of Polynomial Zeros with Weierstrass’ Correction....Pages 153-164
Front Matter....Pages 165-165
Guaranteed Set Computation with Subpavings....Pages 167-178
A New Intersection Algorithm for Parametric Surfaces Based on Linear Interval Estimations....Pages 179-190
Nonlinear State Estimation Using Forward-Backward Propagation of Intervals in an Algorithm....Pages 191-201
Front Matter....Pages 203-203
Interval Methods for Global Optimization Using the Boxing Method....Pages 205-213
A Branch-and-Prune Method for Global Optimization....Pages 215-226
Simulation of a Controlled Aircraft Elevator under Sensor Uncertainties....Pages 227-237
Front Matter....Pages 239-239
Traditional Parameter Estimation Versus Estimation of Guaranteed Parameter Sets....Pages 241-253
Front Matter....Pages 239-239
Stabilizing Control Design of Nonlinear Process Involving Uncertainties....Pages 255-265
Set Estimation, Computation of Volumes and Data Safety....Pages 267-278
Front Matter....Pages 279-279
Verified High-Order Integration of DAEs and Higher-Order ODEs....Pages 281-292
About a Finite Dimensional Reduction Method for Conservative Dynamical Systems and Its Applications....Pages 293-303
Verified Determination of Singularities in Chemical Processes....Pages 305-316
Modeling of Multibody Systems with Interval Arithmetic....Pages 317-327
Front Matter....Pages 329-329
On the algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic....Pages 331-341
Global Random Walk Simulations of Diffusion....Pages 343-354
Interval Computations as a Particular Case of a General Scheme Involving Classes of Probability Distributions....Pages 355-365
For Reliable and Powerful Scientific Computations....Pages 367-377
Reliable Representations of Strange Attractors....Pages 379-390
Back Matter....Pages 391-398
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