An iterative method with truncation for infinite linear systems

摘要

For the infinite linear system Tx = v, where T is an infinite, uniformly strictly diagonally dominant matrix and x and v are infinite vectors, sufficient conditions are imposed on T and v for the existence and uniqueness of a bounded solution. The system is rewritten as x = Ax + b which is first iterated, and then truncated to a finite system. Convergence of the solution of the resulting system to that of the original system is established, and explicit error bounds are determined. Examples are given to illustrate the computation.