Note: interpreting iterative methods convergence with diffusion point of view

TL;DR

This paper offers a diffusion-based interpretation of iterative methods' convergence speeds in solving linear fixed point problems, enhancing understanding of why different schemes converge at varying rates.

Contribution

It introduces a diffusion point of view to analyze and compare the convergence behaviors of various iterative methods.

Findings

Diffusion interpretation clarifies convergence differences among iterative schemes.

Power and Jacobi iterations can converge faster or slower than Gauss-Seidel depending on diffusion dynamics.

Provides insights into optimizing iterative methods based on diffusion analysis.

Abstract

In this paper, we explain the convergence speed of different iteration schemes with the fluid diffusion view when solving a linear fixed point problem. This interpretation allows one to better understand why power iteration or Jacobi iteration may converge faster or slower than Gauss-Seidel iteration.