Convergence Analysis for Nonlinear GMRES
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915633716789248 |
|---|---|
| author | He, Yunhui |
| author_facet | He, Yunhui |
| contents | In this work, we revisit nonlinear generalized minimal residual method (NGMRES) applied to nonlinear problems. NGMRES is used to accelerate the convergence of fixed-point iterations, which can substantially improve the performance of the underlying fixed-point iterations. We consider NGMRES with a finite window size $m$, denoted as NGMRES($m$). However, there is no convergence analysis for NGMRES($m$) applied to nonlinear systems. We prove that for general $m>0$, the residuals of NGMRES($m$) converge r-linearly under some conditions. For $m=0$, we prove that the residuals of NGMRES(0) converge q-linearly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09634 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis for Nonlinear GMRES He, Yunhui Numerical Analysis 65H10 In this work, we revisit nonlinear generalized minimal residual method (NGMRES) applied to nonlinear problems. NGMRES is used to accelerate the convergence of fixed-point iterations, which can substantially improve the performance of the underlying fixed-point iterations. We consider NGMRES with a finite window size $m$, denoted as NGMRES($m$). However, there is no convergence analysis for NGMRES($m$) applied to nonlinear systems. We prove that for general $m>0$, the residuals of NGMRES($m$) converge r-linearly under some conditions. For $m=0$, we prove that the residuals of NGMRES(0) converge q-linearly. |
| title | Convergence Analysis for Nonlinear GMRES |
| topic | Numerical Analysis 65H10 |
| url | https://arxiv.org/abs/2501.09634 |