Recent developments in numerical methods, including advanced iterative solvers and operator preconditioning techniques, have significantly enhanced the accuracy and efficiency of these approaches.

Numerical Solution of Systems of Linear Equations, Iterative Methods Formulation and analysis of basic stationary methods e.g. Gauss-Jacobi, Gauss-Seidel. The numerical solution of Poisson's equation.

We show that the first four iterations produce exactly the same sequence of subspaces as do direct and inverse iteration started from appropriate subspaces. Their convergence properties are therefore ...