Istituto di Informatica e Telematica     
Favati P., Lotti G., Menchi O., Romani F. Solution of Infinite Linear Systems by Automatic Adaptive Iterations. Technical report, 1999.
The problem of approximating the solution of infinite linear systems in sparse block Hessenberg form is considered. Several algorithms are proposed, which do not require special structural properties of the coefficient matrix. These algorithms solve by Gauss-Seidel method a sequence of truncated problems of increasing sizes $n_i$ with not increasing tolerances $10^{-t_i}$. They differ in the way of generating the sequences ${n_i}$ and ${t_i}$. Numerical experiments show that the best trade-off between accuracy and computational cost is reached by choosing the sequence ${t_i}$ in an adaptive way.
Subject G.1.3 Numerical Linear Algebra
65F10 Iterative methods for linear systems

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