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An iterative method approximates a solution by repeatedly updating an initial guess. In numerical linear algebra, a stationary iterative method for a linear system uses a fixed iteration map; other iterations can change their update rule or search space at each step.

A stationary iteration has the formwith a fixed iteration matrix $H$. It converges for every initial vector exactly when the spectral radius satisfies $\rho (H)<1$.

This is an iterative method whose update matrix remains fixed.