# Direct methods

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Direct methods for the solution of the linear system of equations

$\mathbf{A}\mathbf{x} = \mathbf{b}$

obtain an exact solution to the system. The most widely known direct method is Gaussian elimination, which uses elementary matrix operations to compute the solution. Most other direct solution techniques are either a variant of Gaussian elimination or are based upon a particular factorization of the equations that will allow an exact computation. LU decomposition is both a factorization approach and closely related to Gaussian elimination.

Typically, direct methods are best used upon relatively full systems of (the percentage of the elements that are is large) or on banded systems (elements are arranged in diagonal bands).