Abstract
The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. Based on an axiomatic framework we present a convergence analysis of the finite section method for unstructured matrices on weighted lp-spaces. In particular, the stability of the finite section method on l2 implies its stability on weighted lp-spaces. Our approach uses recent results from the theory of Banach algebras of matrices with off-diagonal decay. Furthermore, we demonstrate that Banach algebra theory provides a natural framework for deriving a finite section method that is applicable to large classes of unstructured non-hermitian matrices as well as to least squares problems.
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