| Autor: |
Huang, Na, Dai, Yu-Hong, Orban, Dominique, Saunders, Michael A |
| Rok vydání: |
2022 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| DOI: |
10.13140/RG.2.2.19916.08327 |
| Popis: |
The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous semi-conjugate gradient (SCG) method for unsymmetric positive definite linear systems. Unlike CG, SCG requires the solution of a lower triangular linear system to produce each semi-conjugate direction. We prove that SCG is theoretically equivalent to the full orthogonalization method (FOM), which is based on the Arnoldi process and converges in a finite number of steps. Because SCG's triangular system increases in size each iteration, we study a sliding window implementation (SWI) to improve efficiency, and show that the directions produced are still locally semi-conjugate. A counterexample illustrates that SWI is different from the direct incomplete orthogonalization method (DIOM), which is FOM with a sliding window. Numerical experiments from the convection-diffusion equation and other applications show that SCG is robust and that the sliding window implementation SWI allows SCG to solve large systems efficiently. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
