Successive Over-Relaxation
Successive Over-Relaxation (SOR) is an iterative numerical method used to solve systems of linear equations, particularly those arising from discretized partial differential equations. It is an extension of the Gauss-Seidel method that accelerates convergence by introducing a relaxation parameter, which adjusts the update step to find solutions more efficiently. SOR is widely applied in computational physics, engineering, and scientific computing for problems like heat diffusion, fluid dynamics, and structural analysis.
Developers should learn SOR when working on simulations or numerical models that involve large, sparse linear systems, as it offers faster convergence than basic iterative methods like Jacobi or Gauss-Seidel. It is particularly useful in finite difference or finite element methods for solving PDEs in domains like computational fluid dynamics, electromagnetics, or image processing, where efficiency is critical. Use SOR when you need a balance between computational cost and accuracy in iterative solvers, especially for problems with diagonally dominant matrices.