Jacobi Method
The Jacobi Method is an iterative algorithm used in numerical linear algebra to solve systems of linear equations, particularly for large, sparse matrices. It works by decomposing the matrix into its diagonal and off-diagonal components and iteratively updating the solution vector until convergence. This method is fundamental in computational mathematics and scientific computing for approximating solutions to linear systems.
Developers should learn the Jacobi Method when working on problems involving linear systems in fields like physics simulations, engineering analysis, or machine learning optimization. It is particularly useful for parallel computing applications due to its inherent parallelism, and as a foundational technique for understanding more advanced iterative solvers like the Gauss-Seidel or Successive Over-Relaxation methods.