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For the linear system $\mathbf A \mathbf x = \mathbf b$ generated from 2D Poisson equation using the standard central finite difference method,
$$ \mathbf A = \begin{bmatrix} \mathbf K & -\mathbf I \\ -\mathbf I & \mathbf K & -\mathbf I \\ & -\mathbf I & \mathbf K & -\mathbf I \\ & & \ddots & \ddots & \ddots \end{bmatrix} $$ where $\mathbf I$ is the identity matrix and $\mathbf K$ is the tridiagonal matrix with stencil $[-1 \ 4 \ -1]$.

With Matlab backslash, does anyone know what reordering algorithm matlab will use to solve this sparse system?

And in general, how matlab decide wihch reordering algorithm to use?

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    $\begingroup$ Matlab will likely use (a) minimum degree (MMD) orderings with QR-based \ and /, or (b) COLAMD ordering with the LU-based \ and /, or (c) AMD with Cholesky-based \ and /. Source: the sparse matrix docs and the help page for spparms. To disable the default preordering, run spparms('autoamd',0); spparms('autommd',0). $\endgroup$ – GoHokies Jan 12 '18 at 21:01
  • $\begingroup$ @GoHokies Thanks, it helps a lot $\endgroup$ – user123 Jan 14 '18 at 3:39
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@gohokies has already given the correct answer in a comment, but just for more context: Matlab backslash calls the UMFPACK (now SuiteSparse) solver for sparse linear systems. The default ordering used by UMFPACK is indeed the Approximate Minimum Degree (AMD) method, or a variation thereof.

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