Scientific Computing, Validated Numerics, Interval Methods

1. Front Matter

   Pages i-x

   PDF

2. SCAN 2000 Keynote Address the Future of Intervals

   1. SCAN 2000 Keynote Address the Future of Intervals

      • G. William Walster

      Pages 1-15

3. Software- and Hardware-Tools

   1. Front Matter

      Pages 17-17

      PDF

   2. Variable-Precision Exponential Evaluation

      • Javier Hormigo, Julio Villalba, Michael J. Schulte

      Pages 19-28

   3. Fast Computation of Some Special Integrals of Mathematical Physics

      • Ekatherina A. Karatsuba

      Pages 29-40

   4. Interval Input and Output

      • Eero Hyvönen

      Pages 41-51

   5. A Case for Interval Hardware on Superscalar Processors

      • James E. Stine, Michael J. Schulte

      Pages 53-68

   6. Evaluating the Impact of Accurate Branch Prediction on Interval Software

      • Ahmet Akkas, Michael J. Schulte, James E. Stine

      Pages 69-79

   7. Automatic Test Case Generation Using Interval Arithmetic

      • Günter Schumacher, Armin Bantle

      Pages 81-87

4. Linear Algebra

   1. Front Matter

      Pages 89-89

      PDF

   2. On the Hull of the Solution Sets of Interval Linear Equations

      • Jana Konickova

      Pages 91-102

   3. Computation of Algebraic Solutions to Interval Systems Via Systems of Coordinates

      • Svetoslav Markov

      Pages 103-114

   4. Towards Diagrammatic Analysis of Systems of Interval “Linear Equations”

      • Zenon Kulpa

      Pages 115-126

   5. On the Solution of Parametrised Linear Systems

      • Evgenija D. Popova

      Pages 127-138

5. Polynomials

   1. Front Matter

      Pages 139-139

      PDF

   2. Verified Solutions of Systems of Nonlinear Polynomial Equations

      • Daniela Fausten, Wolfram Luther

      Pages 141-152

   3. Euler-Like Method for the Simultaneous Inclusion of Polynomial Zeros with Weierstrass’ Correction

      • Miodrag S. Petkovic, Dejan V. Vranic

      Pages 153-164

6. Set Enclosures

   1. Front Matter

      Pages 165-165

      PDF

   2. Guaranteed Set Computation with Subpavings

      • Michel Kieffer, Isabelle Braems, Éric Walter, Luc Jaulin

      Pages 167-178

   3. A New Intersection Algorithm for Parametric Surfaces Based on Linear Interval Estimations

      • Katja Bühler, Wilhelm Barth

      Pages 179-190

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.

• AES
• Analysis
• Automat
• Hardware
• Variable
• algorithms
• linear algebra
• modeling
• numerics
• optimization
• scientific computing

• University of Wuppertal, Wuppertal, Germany

  Walter Krämer

• University of Würzburg, Würzburg, Germany

  Jürgen Wolff Gudenberg

Policies and ethics