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Iterative method
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====Examples==== Basic examples of stationary iterative methods use a splitting of the matrix <math> A </math> such as :<math> A = D+L+U\,,\quad D := \text{diag}( (a_{ii})_i) </math> where <math> D </math> is only the diagonal part of <math> A </math>, and <math> L </math> is the strict lower [[Triangular matrix|triangular part]] of <math> A </math>. Respectively, <math> U </math> is the strict upper triangular part of <math> A </math>. * [[Modified Richardson iteration|Richardson method]]: <math> M:=\frac{1}{\omega} I \quad (\omega \neq 0) </math> * [[Jacobi method]]: <math> M:=D </math> * [[Jacobi method#Weighted Jacobi method|Damped Jacobi method]]: <math> M:=\frac{1}{\omega}D \quad (\omega \neq 0) </math> * [[Gauss–Seidel method]]: <math> M:=D+L </math> * [[Successive over-relaxation|Successive over-relaxation method]] (SOR): <math> M:=\frac{1}{\omega}D+L \quad (\omega \neq 0) </math> * [[Symmetric successive over-relaxation]] (SSOR): <math> M := \frac{1}{\omega (2-\omega)} (D+\omega L) D^{-1} (D+\omega U) \quad (\omega \not \in \{0,2\}) </math> Linear stationary iterative methods are also called [[Relaxation (iterative method)|relaxation methods]].
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