§ _-Phiãó6—dZddlmZddlmZddlmZgd¢ZdS)aÅRelaxation methods. The multigrid cycle is formed by two complementary procedures: relaxation and coarse-grid correction. The role of relaxation is to rapidly damp oscillatory (high-frequency) errors out of the approximate solution. When the error is smooth, it can then be accurately represented on the coarser grid, where a solution, or approximate solution, can be computed. Iterative methods for linear systems that have an error smoothing property are valid relaxation methods. Since the purpose of a relaxation method is to smooth oscillatory errors, its effectiveness on non-oscillatory errors is not important. This point explains why simple iterative methods like Gauss-Seidel iteration are effective relaxation methods while being very slow to converge to the solution of Ax=b. PyAMG implements relaxation methods of the following varieties: 1. Jacobi iteration 2. Gauss-Seidel iteration 3. Successive Over-Relaxation 4. Polynomial smoothing (e.g. Chebyshev) 5. Jacobi and Gauss-Seidel on the normal equations (A.H A and A A.H) 6. Krylov methods: gmres, cg, cgnr, cgne 7. No pre- or postsmoother Refer to the docstrings of the individual methods for additional information. é)Ú chebyshev)Ú relaxation)Ú smoothing)rrrÚutilsN)Ú__doc__ÚrrrÚ__all__©óúY/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/relaxation/__init__.pyúr sXðððð8ÐÐÐÐÐØÐÐÐÐÐØÐÐÐÐÐð <Ð ;Ð ;€€€r