| | |
| | |
Stat |
Members: 3645 Articles: 2'506'133 Articles rated: 2609
28 April 2024 |
|
| | | |
|
Article overview
| |
|
Weighted Inner Products for GMRES and Arnoldi Iterations | Mark Embree
; Ronald B. Morgan
; Huy V. Nguyen
; | Date: |
1 Jul 2016 | Abstract: | The convergence of the restarted GMRES method can be significantly improved,
for some problems, by using a weighted inner product that changes at each
restart. How does this weighting affect convergence, and when is it useful? We
show that weighted inner products can help in two distinct ways: when the
coefficient matrix has localized eigenvectors, weighting can allow restarted
GMRES to focus on eigenvalues that otherwise slow convergence; for general
problems, weighting can break the cyclic convergence pattern into which
restarted GMRES often settles. The eigenvectors of matrices derived from
differential equations are often not localized, thus limiting the impact of
weighting. For such problems, incorporating the discrete cosine transform into
the inner product can significantly improve GMRES convergence, giving a method
we call W-GMRES-DCT. Integrating weighting with eigenvalue deflation via
GMRES-DR also can give effective solutions. Similarly, weighted inner products
can be combined with the restarted Arnoldi algorithm for eigenvalue
computations: weighting can enhance convergence of all eigenvalues
simultaneously. | Source: | arXiv, 1607.0255 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |