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Other applications of the method

A similar technique can be used for any iterative method. If the original iteration had the form

then the modified version would use

However, the formulation presented above, used for solving systems of linear equations, is not a special case of this formulation if x is considered to be the complete vector. If this formulation is used instead, the equation for calculating the next vector will look like

where L ∗ = L + D {\displaystyle L_{*}=L+D}. Values of ω > 1 {\displaystyle \omega >1} are used to speed up convergence of a slow-converging process, while values of ω < 1 {\displaystyle \omega <1} are often used to help establish convergence of a diverging iterative process or speed up the convergence of an overshooting process.

There are various methods that adaptively set the relaxation parameter ω {\displaystyle \omega } based on the observed behavior of the converging process. Usually they help to reach a super-linear convergence for some problems but fail for the others.