Projected iterative algorithms with application to multicomponent transport

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.