A Survey on Intelligent Iterative Methods for Solving Sparse Linear Algebraic Equations

TL;DR

This survey reviews intelligent iterative methods for solving large-scale sparse linear equations, highlighting their development, components, and parameters, and discusses future research directions in the field.

Contribution

It provides a comprehensive overview of recent advances in intelligent iterative methods and proposes new directions for future research in this area.

Findings

Intelligent iterative methods improve efficiency by optimizing parameters and components.

Deep learning enhances the adaptability of iterative solvers.

The survey identifies key challenges and potential research avenues.

Abstract

Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods have lower computational complexity and memory consumption, and are thus often used to solve large-scale sparse linear equations. However, there are numerous iterative methods, parameters and components needed to be carefully chosen, and an inappropriate combination may eventually lead to an inefficient solution process in practice. With the development of deep learning, intelligent iterative methods become popular in these years, which can intelligently make a sufficiently good combination, optimize the parameters and components in accordance with the properties of the input matrix. This survey then reviews these intelligent iterative methods. To be clearer, we shall divide our discussion into three aspects: a method aspect, a component aspect and a parameter aspect. Moreover, we summarize the existing work and propose potential research directions that may deserve a deep investigation.