Two stable modifications of the finite section method

TL;DR

This paper introduces and compares two stable modifications of the finite section method for band-dominated operators, providing explicit criteria for their applicability when the classical method is unstable.

Contribution

It presents two novel modifications of the finite section method with explicit applicability criteria for unstable cases.

Findings

Both methods are demonstrated to be effective in cases where the classical method fails.

Explicit criteria for the applicability of each modified method are provided.

The modifications improve stability in the finite section approach for band-dominated operators.

Abstract

In this article we demonstrate and compare two modified versions of the classical finite section method for band-dominated operators in case the latter is not stable. For both methods we give explicit criteria for their applicability.