2006/10/19 by Karlheinz Gr, Gröchenig, Karlheinz, Ziemowit Rzeszotnik +3
Computer Science · Mathematics · Physics and Astronomy · #47L80 #65J10 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.math/0610588
openalex publication_date 2006/10/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. We present quantitative estimates for the rate of the convergence of the finite section method on weighted ℓ p-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 non-hermitian matrices. An example from digital communication illustrates the practical usefulness of the proposed theoretical framework.