5.1 Rutishauser の計算式

$\displaystyle z$	$\displaystyle =$	$\displaystyle \frac{a_{qq}-a_{pp}}{2a_{pq}}\quad(=\cot2\theta),$
$\displaystyle t$	$\displaystyle =$	$\displaystyle \frac{\sign(z)}{\vert z\vert+\sqrt{1+z^2}}\quad(=\tan\theta),$
$\displaystyle c$	$\displaystyle =$	$\displaystyle \frac{1}{\sqrt{1+t^2}}\quad(=\cos\theta),$
$\displaystyle s$	$\displaystyle =$	$\displaystyle c t\quad(=\sin\theta),$
$\displaystyle u$	$\displaystyle =$	$\displaystyle \frac{s}{1+c}\quad(=\tan\theta/2),$
$\displaystyle b_{pp}$	$\displaystyle =$	$\displaystyle a_{pp}-t a_{pq},$
$\displaystyle b_{qq}$	$\displaystyle =$	$\displaystyle a_{qq}+t a_{pq},$
$\displaystyle b_{pq}$	$\displaystyle =$	$\displaystyle b_{qp}=0,$
$\displaystyle b_{pj}$	$\displaystyle =$	$\displaystyle b_{jp}=a_{pj}-s(a_{qj}+u a_{pj})$ $\displaystyle \mbox{($j\ne p,q$)}$ $\displaystyle ,$
$\displaystyle b_{qj}$	$\displaystyle =$	$\displaystyle b_{jq}=a_{qj}+s(a_{pj}-u a_{qj})$ $\displaystyle \mbox{($j\ne p,q$)}$ $\displaystyle .$