Session title:

Approximate Algebraic Computation: towards Symbolic-Numeric Algorithms.

a) What is APPROXIMATE ALGEBRAIC COMPUTATION 

  In conventional computer algebra, we mostly aim at performing
  algebraic computation exactly on the basis of rational number
  arithmetic and the introduction of algebraic and transcendental numbers.

  But many problems coming from areas like computer vision, robotics,
  computational biology, physics, ... are described with incertitudes on the
  input parameters or coefficients.
  In this context, the usual exact algorithms of computer algebra are not 
  applicable.

  The recent years have witnessed the emergence of new researches
  combining symbolic-numeric computations and leading to new kinds of 
  algorithms, involving algebraic computations with approximate numeric
  arithmetic, such as floating-point number arithmetic.  

  We call computations with such algorithms AAC (Approximate Algebraic 
  Computation).
  
  On the basis of such algebraic operations, new problems are occurring,
  new points of view are coming forth and new approaches are being developed.

  Symbolic-Numeric Algebra for Polynomials is one of the most 
  rapidly developing area of approximate algebraic computation.

  This is topic of this session.

b) Problems to be discussed in the session

  Approximate algebraic computation will have a large potentiality for
  many application problems, because they are quite efficient in both
  computation time and space.  However, research is in the infancy stage
  and we have so many problems.
  In this session, we will focus our attention (but not restrictively) on
  instability problems, static and dynamic error analysis, certification of
  the output, continuity, flatness, ... and also on algorithmic
  development, system building and applications.

c) Typical subjects to be discussed

  Approximate GCD, approximate factorization, ...
  How to solve polynomial equations with inexact coefficients
      especially how to solve multivariate polynomial systems.
  Connections between commutative algebra and numerical computations.
  Error analysis of algorithms and stabilization techniques, 
  Certification of the output. 
  Application of approximate algebraic computation such as
      hybrid integration and rational function approximation,
  Software systems for approximate algebraic computation.
  Examples of Symbolic-Numeric Applications ...