# Direct methods

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 Revision as of 00:20, 19 December 2005 (view source)Jasond (Talk | contribs)← Older edit Latest revision as of 05:19, 24 May 2007 (view source)Tsaad (Talk | contribs) (creating links inside each header section) Line 6: Line 6: 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). 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). + + # [[Gaussian elimination]] + # [[LU decomposition]] + # [[Tridiagonal matrix algorithm - TDMA (Thomas algorithm)]]

## Latest revision as of 05:19, 24 May 2007

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).