How does matlab solve large, symmetric and sparse linear systems?

Etc.). CHOLMOD, UMFPACK and qr factorization are some of the options.

If the matrix is sparse and symmetric positive definite, but has a very narrow band, then a specialized band solver is used. Most matrices do not have a narrow enough band to trigger this condition. Typically, this comes up with 1D splines in the Spline Toolbox.

2D problems have a large 'band' (they are not truly banded matrices).

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