Science Score: 31.0%
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Low similarity (6.5%) to scientific vocabulary
Repository
Matlab Codes of SWI, DIOM, DQGMRES
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Metadata Files
README.md
MATLAB code of some Krylov methods for solving unsymmetric positive definite linear systems
How to cite
If you use swi in your work, please cite using the format given in CITATION.bib
Content
We provide here some matlab code of certain methods for solving unsymmetric positive definite linear systems Ax = b.
Algorithms
- REGMRES Restarted GMRES (REGMRES) (Algorithm 6.11 in Yousef Saad's Iterative Methods for Sparse Linear System (2nd Edition)) (When restart=n, it equals to GMRES).
- REFOM Restarted Full Orthogonalization Method (Algorithms 6.5 in Yousef Saad's Iterative Methods for Sparse Linear System (2nd Edition)) (When restart=n, it equals to FOM).
- RESCG Restarted Semi-Conjugate Gradient Method (When restart=n, it equals to SCG).
- DQGMRES Direct Quasi-GMRES (DQGMRES) (Algorithms 6.6 and 6.13 in Yousef Saad's Iterative Methods for Sparse Linear System (2nd Edition)) (When m=n, it equals to GMRES).
- DIOM Direct Incomplete Orthogonalization Method (Algorithms 6.6 and 6.8 in Yousef Saad's Iterative Methods for Sparse Linear System (2nd Edition)) (When m=n, it equals to FOM).
- SWI Sliding Window Implementation of SCG with pre-allocated memory (When m=n, it equals to SCG).
- DYNSWIWP Sliding Window Implementation of SCG with choosing m dynamically.
Test
Convection-diffusion
The linear system arises from the convection diffusion equation. - test_condiff Runing this file gets the comparing results, for more details, please see test_condiff.pdf
SuiteSparse Matrix
We select matrices from the SuiteSparse Matrix Collection and b = Ax* with x* = (1,1,...,1)'. - test_suitesparse.m Runing this file gets the comparing results, for more details, please see test_suitesparse.pdf. - testproblem.txt Storing all the file name of testing matrices.
Citation (CITATION.bib)
@Misc{huang-dai-Orban-Saunders-swi,
author={Huang, Na and Dai, Yu-Hong and Orban, Dominique and Saunders, Michael A},
title={{MATLAB} code of some {K}rylov methods for solving unsymmetric positive definite linear systems},
month = {June},
howpublished = {https://github.com/huangna112/SWI},
year = {2022},
DOI = {10.5281/zenodo.6679527},
}