Title  
Approximate Algebraic Computation 

Organizers  
Robert M. Corless ( University of Western Ontario, rcorless@uwo.ca ) Tateaki Sasaki ( University of Tsukuba, sasaki@math.tsukuba.ac.jp ) MatuTarow Noda ( Ehime University, noda@cite.ehimeu.ac.jp ) Kiyoshi Shirayanagi ( NTT Corporation, shirayan@theory.brl.ntt.co.jp ) 

Aim and Scope  
In conventional computer algebra, the usual aim is to perform algebraic
computation exactly using rational number arithmetic and the introduction
of algebraic and transcendental numbers. But many problems coming from
areas like computer vision, robotics, computational biology, physics, etc,
are described with inexact numbers ("empirical" numbers) as the
input parameters or coefficients. In this context, the usual exact algorithms
of computer algebra may not be easily applicable, or may be inefficient.
Recent years have witnessed the emergence of new research combining symbolicnumeric
computations and leading to new kinds of algorithms, involving algebraic
computations with approximate numeric arithmetic, such as floatingpoint
number arithmetic. A typical example of the new research is SNAP (SymbolicNumeric
Algebra for Polynomials, also called Numerical Polynomial Algebra) which
is increasingly becoming active. New workshop SNAP (SymbolicNumeric Computation)
will be held in this July. The concept of AAC (Approximate Algebraic Computation)
is strongly related to SNAP and SNC. The aim of this session is not only
to discuss problems in AAC, but also to make interaction between AAC to
create even more powerful theories and realworld applications. Of course,
discussions from SNAP and/or SNC are extremely welcome. In the future,
it would be wonderful if researches from AAC, SNAP, SNC and others could
be combined into a new scientific computing to support a reliable and satisfying
network society. Problems to be discussed in the session: Approximate algebraic computation, stabilization and regularization have great potential for many application problems, because they are quite efficient in both computation time and space while attaining useful accuracy. However, research is still in an early stage and many problems remain open. 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. Typical subjects to be discussed


List of talks  
