\[\begin{bmatrix}-b_{1}&a_{1}&&&0\\
c_{2}&-b_{2}&a_{2}\\
&\ddots&\ddots&\ddots\\
&&c_{N-2}&-b_{N-2}&a_{N-2}\\
0&&&c_{N-1}&-b_{N-1}\end{bmatrix}\begin{bmatrix}w_{1}^{(N)}\\
w_{2}^{(N)}\\
\vdots\\
w_{N-2}^{(N)}\\
w_{N-1}^{(N)}\end{bmatrix}=\begin{bmatrix}d_{1}-c_{1}\lambda\\
d_{2}\\
\vdots\\
d_{N-2}\\
d_{N-1}\end{bmatrix}.\]