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5.1 Rutishauser の計算式

$ \theta$ atan() を用いて求めたりする必要はない。


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


next up previous contents
Next: 5.2 MATLAB での実験 Up: 5 Jacobi 法 Previous: 5 Jacobi 法
桂田 祐史
2015-12-22