Discrete Poisson equation: Difference between revisions

m
A and D are matrices and do not need to be enclosed by brackets
(→‎Example: Had to change sign here to.)
m (A and D are matrices and do not need to be enclosed by brackets)
 
:<math>
U =
\begin{bmatrix} U \end{bmatrix} =
\begin{bmatrix} u_{22}, u_{32}, u_{42}, u_{23}, u_{33}, u_{43}, u_{24}, u_{34}, u_{44}
\end{bmatrix}^{T}
== Methods of solution ==
 
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]], [[cyclic reduction]], [[successive overrelaxation]], and [[Fourier transform]]s. A theoretically optimal <math> O(n) </math> solution can also be computed using [[multigrid methods]].