Organisers: Thomas Lickteig and Marie-Francoise Roy.
Organisers: Felipe Cucker and Herb Keller.
The common denominator of the talks was the complexity of algebraic equations solving, including upper and lower bounds. A subject which has attracted the attention during the last years, and was therefore present at the workshop, was the consideration of the condition number of a system as a complexity parameter measuring the efficiency of homotopy methods. Another topic widely represented was the study of sparse (toric) systems. Advances on classical problems (Newton's method for one variable polynomials, homotopy methods, relations between complexity classes) were also presented. P.Koiran's talk deserves a special mention since it was awarded during the conference with the "1996 Best Paper Award" of the Journal of Complexity. The talk presented an algorithm which decides the existence of complex zeros of polynomial systems which doesn't rely on the classical elimination arguments but on number theory ones.
Organisers: Erich Novak and Henryk Wozniakowski.
This workshop consisted of 12 talks. The following subjects were, in particular, covered:
Some of the talks were attended by many participants from other workshops.
Erich Novak
Organisers: Jim Demmel and Alan Edelman.
The workshop concentrated on state of the art mathematical techniques for iterative methods, multilevel methods and eigenvalue approaches. Other talks were devoted to applications in imaging, optimization and fundamental issues for linear algebra. The variety of subjects covered show how the area of numerical linear algebra has penetrated into so many fields of research continuing to draw strength from mathematical foundations and inspiration from important applications. This theme was evident in all of the talks.
Organisers: Wolfang Dahmen and Ron DeVore.
The main topics of the workshop were Finite Element analysis, efficient finite difference methods and well posedness for hyperbolic problems, inverse problems and multiscaled techniques for the fast solution of corresponding discrete problems. Primary emphasis was put on intertwining concepts from constructive approximation theory with the underlying analytical or physical problem. Typical examples are preconditioning and compression techniques. Essential ingredients are certain pairs of direct and inverse estimates which ultimately give rise to the validity of norm equivalence for scales of Sobolev and Besov spaces in term of approximation properties., the corresponding Besov regularity theory for elliptic PDEs and the analysis of adaptive solvers. This is relevant for practical realizations and may also offer conceptual input for complexity theory.
Organisers: Clovis Gonzaga and Mike Todd.
Organisers: Arieh Iserles and Andrew Stuart.
Two main themes of the workshop were symplectic discretization of Hamiltonian differential systems and the numerical analysis of ordinary differential equations on differential manifolds. Other talks were devoted to computational dynamics and to numerical issues originating in control theory, inverse eingenvalue problems for PDEs and inverse scattering. The breakdown of subjects reflects very recent developments and change of emphasys at the interface of nonlinear dynamical systems and the numerical analysis of differential equations. While the emphasis in the last decade was often on nonlineal stability theory and on the recovery of complicated dynamical behavior under descretization, many of these problems have now been adequately resolved. A new major trend concerns itself with the recovery of invariance by numerical solutions and this was the broad common denominator to many of the talks in this workshop.
Organisers: Lenore Blum and Imre Simon.
The workshop tried to focus on some themes in Theoretical Computer Science which need or might need in the future computer assistance for symbolic computations. A typical example was given by Jean-Eric Pin's lecture on Computations in a Finite Semigroup. Other topics covered included quantum computing and a few combinatorially oriented talks.
Imre Simon
Organisers: Jean-Michel Morel and David Mumford. Back to the FoCM'97 home page
Back to the FoCM'97 home page