Mathematics-Online lexicon: Givens Elimination for Tridiagonal Systems

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	Mathematics-Online lexicon:
	Givens Elimination for Tridiagonal Systems

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overview

A tridiagonal linear system,

$\displaystyle \left( \begin{array}{ccccc} d_1 & v_1 & & & 0 \\ u_2 & \ddots ... ...egin{array}{c} b_1 \\ \vdots \\ \vdots \\ \vdots \\ b_n \end{array} \right)$

can be solved with the aid of

Givens transformations. The $\ell$ -th transformation modifies rows $\ell$ and $\ell+1$ of the system, annihilating the subdiagonal coefficient $u_{\ell+1}$ and generating an additional non-zero coefficient in position $(\ell,\ell+2)$ . The resulting upper triangular system is solved with backward substitution.

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automatically generated 3/ 8/2007