tridiagonal-symmetric-system-of-linear-equations

This script solves systems of linear equations with tridiagonal symmetric matrices. Therefore insert your diagonal (a), upper diagonal (u) and RHS (b) vectors in the first few lines of the code and execute it. The equation should look something like this:

$$ \begin{bmatrix} a_{0} & u_{0} & 0 & \dots & 0 \\ u_{0} & a_{1} & u_{1} & \ddots & \vdots \\ 0 & u_{1} & a_{2} & u_{2} & 0 \\ \vdots & \ddots & \ddots & \ddots & \ddots \\ 0 & \dots & 0 & u_{n-2} & a_{n-1} \end{bmatrix} \cdot \begin{bmatrix} c_{0} \\ c_{1} \\ \\ \vdots \\ c_{n-1} \end{bmatrix} =\begin{bmatrix} b_{0} \\ b_{1} \\ \\ \vdots \\ b_{n-1} \end{bmatrix} \in \mathbb{R}^{n}$$

Since using Gaussian eliminiation would lead to $\mathcal{O}(n^3)$ this algorithm is much faster with $\mathcal{O}(n)$ and explicitly $8n-6$ operations.