# Computing the lowest eigenvalues of the Fermion matrix by subspace iterations

## TL;DR

The paper presents a subspace iteration method for efficiently computing multiple lowest eigenvalues of large Hermitean matrices, showing that increasing the number of eigenvalues does not significantly raise computational costs.

## Contribution

It introduces a subspace iteration approach that efficiently computes multiple eigenvalues simultaneously without substantial additional computational effort.

## Key findings

- Computational cost remains nearly constant as the number of eigenvalues increases.
- Multiple eigenvalues can be obtained at almost no extra cost compared to computing a single eigenvalue.
- The method is effective for large, sparse Hermitean matrices.

## Abstract

Subspace iterations are used to minimise a generalised Ritz functional of a large, sparse Hermitean matrix. In this way, the lowest $m$ eigenvalues are determined. Tests with $1 \leq m \leq 32$ demonstrate that the computational cost (no. of matrix multiplies) does not increase substantially with $m$. This implies that, as compared to the case of a $m=1$, the additional eigenvalues are obtained for free.