Finite sections of random Jacobi operators
It provides a theoretical foundation for truncation methods in numerical analysis of random operators, which is relevant for researchers working on infinite-dimensional systems with stochastic coefficients.
The paper studies the finite section method for solving infinite linear equations with random Jacobi operators, proving that the truncation technique converges almost surely for non-selfadjoint operators and simplifies in the self-adjoint case.
This article is about a problem in the numerical analysis of random operators. We study a version of the finite section method for the approximate solution of equations $Ax=b$ in infinitely many variables, where $A$ is a random Jacobi operator. In other words, we approximately solve infinite second order difference equations with stochastic coefficients by reducing the infinite volume case to the (large) finite volume case via a particular truncation technique. For most of the paper we consider non-selfadjoint operators $A$ but we also comment on the self-adjoint case when simplifications occur.