Taylor Model Mini Workshop - Miami Beach, December 16 20, 2002
Meeting Schedule (The meeting room is Imperial IV. The room is accessible until 9pm.)
Talk sessions: 9:00 to 12:00, 5:00 to 7:00
Talks are free style, namely questions and discussions are encouraged during the talks.
Each talk can be from 15 minutes to 90 minutes. The talk schedule will be adjusted.
Group Work sessions: in the afternoon, possibly including Monday.
We will have about 5 work groups (See below). Each group works on its own.
We will schedule each day's active work groups at the meeting depending on the situation.
Date Morning (9:00 - noon) Evening (5:00 to 7:00)  
     
12/16 (Monday) Taylor model basics Accuracy of Computation
  Interval arithmetics and packages Code Demos etc.
  Accuracy of Computation (- continues to the afternoon) Work Groups
12/17 (Tuesday) Other data types (Complex Taylor models) Work Groups
  Range Bounding (LDB, TB) Code Demos
     
12/18 (Wednesday) ODE Work Groups
     
     
12/19 (Thursday) PDE, DAE, ODE Work Groups
  The other Applications  
     
12/20 (Friday) Other Topics Work Groups
     
     
12/21 (Saturday) Supplemental Work Groups
   
supplemental, optional ( For people still staying in Miami to work. Revol, Berz, Makino, Grote, ...)
Work Groups
A: Variable precision, Intervals, Validation
B: Range Bounding
C: ODEs
D: PDEs, DAEs, Control
E: Nonlinear equations, Implicit equations, Algebraic Constraint
F: Students Group? (Ingo Eble, Johannes Grote, Youn-Kyung Kim, Jun Yu )
Talks
12/16 (Monday)
Makino Introduction
Berz and/or Makino Taylor Model basics
Nathalie Revol Rigorous validation of arithmetic, accuracy of Fortran intrinsics
George Corliss Philosophy of how to check validated codes
Louis Rall "Algorithm Transformation"
Berz and/or Makino TMs and other Polynomial Methods
12/17 (Tuesday)
Alexandre Ovsiannikov Complex Taylor models
Youn-Kyung Kim/Makino Comparison of TM range bounding with other state of the art methods
P.S.V. Nataraj Range bounding for polynomials using Bernstein forms
Intro_bernstein.pdf
Higher order convergence using combined TB-forms
Jun Yu Results of code validation tests (COSY, SUN Fortran,...)
12/18 (Wednesday)
Berz/Makino COSY TM Cosine-example
George Corliss Error handling
Berz/Makino Validated ODE integration with Taylor models.
Markus Neher "A priori enclosures for ODEs: an alternative to fixed point theorems"
Warwick Tucker Interesting ODE problems in theorem proving, and what they need
Everglades Excursion
12/19 (Thursday)
Piotr Zgliczynski "Rigorous numerics and computer assisted proofs for dissipative PDEs"
additional data for the talk
additional tables for the talk
Paper with proofs from the talk
Berz Controlling the Wrapping Effects
P.S.V. Nataraj Global Optimization
12/20 (Friday)
Makino TM ODE linear example
Louis Rall Fourier transformation
Most of the talks of M.Berz and K. Makino are linked to the following paper:
Taylor Models and other Validated Functional Inclusion Methods
which can be found on our Beam Theory Group Publications website