# An Inexact Inverse Power Method for Numerical Analysis of Stochastic Dynamic Systems

## TL;DR

This paper introduces an inexact inverse power method (IIPM) for efficiently computing partial eigenvalues of large sparse matrices, demonstrating its advantages in stochastic dynamic systems analysis.

## Contribution

The paper presents a novel IIPM that uses low precision inner solutions, requiring less memory and offering improved convergence over existing methods.

## Key findings

- IIPM effectively computes eigenvalues in large-scale stochastic systems.
- The method outperforms inexact Rayleigh quotient and Jacobi-Davidson methods.
- Computational results confirm IIPM's efficiency and usefulness.

## Abstract

This paper proposes an efficient method for computing partial eigenvalues of large sparse matrices what can be called the inexact inverse power method (IIPM). It is similar to the inexact Rayleigh quotient method and inexact Jacobi-Davidson method that it uses only a low precision approximate solution for the inner iteration. But this method uses less memory than inexact Jacobi-Davidson method and has stronger convergence performance than inexact Rayleigh quotient method. We exemplify the advantages of IIPM by applying it to find the ground state in theory of stochastics. Here we need to solve hundreds of large-scale matrix. The computational results show that this approach is a particularly useful method.