1998 IMACS Conference on Applications of Computer Algebra
In the conventional computer algebra, we mostly aimed at performing algebraic computation exactly on the basis of the rational number arithmetic and introduction of algebraic and transcendental numbers. About ten year ago, some reseachers began to perform algebraic compu- tations with approximate numeric arithmetic, such as floating-point number arithmetic, and they developed algorithms of approximate GCD, approximate factorization, etc., of polynomials. On the basis of such basic algebraic operations, researchers have begun to construct new algorithms of symbolic-numeric combined type. We call computa- tions with such algorithms approximate algebraic computation.
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 infacncy stage and we have so many problems, in particular, approximate algebraic algorithms aften show instability. Therefore, in this session, we focus our attention on not only algorithms development and system building but also error analysis and stabilization of algorithms.
Approximate GCD and approximate factorization, How to solve polynomial equations with inexact coefficients especially how to solve multivatiate polynomial systems, Error analysis of algorithms and stabilization techniques, Application of approximate algebraic computation such as hybrid integration and rational function approximation, Software systems for approximate algebraic computation.