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Givens Elimination for Tridiagonal Systems


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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 $ n-1$ 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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( .m, 444 ,  08.03.2007)

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  automatically generated 3/ 8/2007