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