Discrete Poisson equation: Difference between revisions

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Because <math> \begin{bmatrix} A \end{bmatrix} </math> is block tridiagonal and sparse, many methods of solution
have been developed to optimally solve this linear system for <math> \begin{bmatrix} U \end{bmatrix} </math>.
Among the methods are a generalized [[Thomas algorithm]] with a resulting computational complexity of <math> O(n^{2}) </math>, [[cyclic reduction]], [[successive overrelaxation]] that has a complexity of <math> O(n^{1.5}) </math>, and [[Fourier transform]]s. Awhich is <math> O(n log(n)) </math>. theoreticallyAn optimal <math> O(n) </math> solution can also be computed using [[multigrid methods]].
== Applications ==
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