PROJECTED ITERATIVE ALGORITHMS

         WITH APPLICATION TO MULTICOMPONENT TRANSPORT



                        (1,2,3)                        (3)
           Alexandre ERN            Vincent GIOVANGIGLI



(1):  CERMICS-ENPC, La Courtine, 93167 Noisy-Le-Grand Cedex, France
(2):  Yale University, Department of Mechanical Engineering, USA
(3):  CMAP-CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France




We investigate projected iterative algorithms for solving
constrained symmetric singular linear systems. 
We discuss the symmetry of generalized inverses and 
investigate projected standard iterative methods
as well as projected conjugate gradient algorithms.
Using a generalization of Stein's theorem for
singular matrices, we obtain a new proof of Keller's theorem.
We also strengthen a result from Neumann and Plemmons 
about the spectrum of iteration matrices.
As an application, we consider the linear systems 
arising from the kinetic theory of gases
and providing transport coefficients 
in multicomponent gas mixtures.
We obtain low-cost accurate approximate
expressions for the transport coefficients that can be used in 
multicomponent flow models.
Typical examples  for the species diffusion coefficients and 
the volume viscosity are presented.


Rapport interne CMAP 312, 1995
Linear Algebra and its Applications, 1995, sous presse.


E-mail:  ern@cmapx.polytechnique.fr
         giovangi@cmapx.polytechnique.fr