Coarse grid corrections in Krylov subspace evaluations of the matrix exponential
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914762910072832 |
|---|---|
| author | Botchev, Mike A. |
| author_facet | Botchev, Mike A. |
| contents | A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $φ$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with these functions. It is based on splitting the vector by which the matrix function is multiplied into a smooth part and a remaining part. The smooth part is then handled on a coarser grid, whereas the computations on the original grid are carried out with a relaxed stopping criterion tolerance. Estimates on the error are derived for the two-grid and multigrid variants of the proposed CGC algorithm. Numerical experiments demonstrate the efficiency of the algorithm, when employed in combination with Krylov subspace and Chebyshev polynomial expansion methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_07590 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Coarse grid corrections in Krylov subspace evaluations of the matrix exponential Botchev, Mike A. Numerical Analysis Computational Physics 65F60, 65M20, 65M55 A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $φ$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with these functions. It is based on splitting the vector by which the matrix function is multiplied into a smooth part and a remaining part. The smooth part is then handled on a coarser grid, whereas the computations on the original grid are carried out with a relaxed stopping criterion tolerance. Estimates on the error are derived for the two-grid and multigrid variants of the proposed CGC algorithm. Numerical experiments demonstrate the efficiency of the algorithm, when employed in combination with Krylov subspace and Chebyshev polynomial expansion methods. |
| title | Coarse grid corrections in Krylov subspace evaluations of the matrix exponential |
| topic | Numerical Analysis Computational Physics 65F60, 65M20, 65M55 |
| url | https://arxiv.org/abs/2107.07590 |