Infinite Matrices and their Finite Sections, 2006
An Introduction to the Limit Operator Method
Frontiers in Mathematics Series

This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering.

A fascinating topic at the interface of functional analysis, algebra and numerical analysis

Presents a recently developed and powerful tool for the understanding of the connection between large finite matrices and their infinite counterparts

A very readable presentation (many figures, remarks, examples, and a refreshing amount of informal explanantions of the results)

Includes supplementary material: sn.pub/extras