Solution of infinite linear systems by automatic adaptive iterations (Q1590658)

The iterative solution of infinite linear systems with sparse coefficient matrices in block Hessenberg form are discussed. Examples of such systems are derived from the discretization of partial differential equations on unbounded domains or those describing the steady-state distribution of Markov chains. A family of algorithms based on Gauss-Seidel iteration is introduced. Two types of convergence are investigated: weak convergence and strong convergence. Numerical experiments are performed on a set of test problems including both differential and stochastic problems.