An Error Bound for Certain Successive Overrelaxation Schemes
Theodore R. Hatcher · SIAM Journal on Numerical Analysis · 1982
Suppose $Ax = k$ is a system of linear equations where the matrix A is obtained from a finite difference approximation to an elliptic boundary value problem. This paper gives a bound for the norm of $\varepsilon _n = x - x_n $ in terms of the norms of $\delta _n = x_n - x_{n - 1} $ and $\delta _{n + 1} = x_{n + 1} - x_n $ and their inner product, where $x_n $ is the nth iteration vector obtained using the successive overrelaxation method.