# Spectral and norm estimates for matrix sequences arising from a finite difference approximation of elliptic operators

Source: [Spectral and norm estimates for matrix sequences arising from a finite difference approximation of elliptic operators](<https://www.sota2.com/research/paper/68fa5a2c1e209131ce9bd964>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T16:20:39.291Z

Authors: Armando Coco, Sven-Erik Ekstr\\"om, Giovanni Russo, Stefano Serra-Capizzano, Santina Chiara Stissi

Published: 2021-08-20T09:48:25.000Z

## Abstract

When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for matrix sequences arising from the approximation of the Laplacian via ad hoc finite differences. The analysis involves several tools from matrix theory and in particular from the setting of Toeplitz operators and Generalized Locally Toeplitz matrix sequences. Several numerical experiments are conducted, which confirm the correctness of the theoretical findings.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2108.09086>)

[PDF](<https://arxiv.org/pdf/2108.09086.pdf>)