# GMRES with Singular Vector Approximations

## TL;DR

This paper introduces an enhanced GMRES method that incorporates approximate right singular vectors into Krylov subspaces to improve convergence by reducing error norms, demonstrated through numerical experiments on benchmark matrices.

## Contribution

The paper presents a novel GMRES variant that augments Krylov subspaces with approximate singular vectors, offering improved error suppression over standard methods.

## Key findings

- The proposed method outperforms standard GMRES in reducing error norms.
- Numerical experiments validate the effectiveness of the singular vector augmentation.
- The approach compares favorably with GMRES methods using eigenvectors.

## Abstract

This paper has proposed the GMRES that augments Krylov subspaces with a set of approximate right singular vectors. The proposed method suppresses the error norms of a linear system of equations. Numerical experiments comparing the proposed method with the Standard GMRES and GMRES with eigenvectors methods[3] have been reported for benchmark matrices.