6.3 Gauß elimination of tridiagonal matrices

Let $A$ positive definite and tridiagonal and we want to solve the system of equations

$$A \cdot \underline{x} \;=\;\underline{f}$$

via Gauß elimination.

The sequential and vectorized version of the Gauß elimination with tridiagonal matrices is easy to implement. Fig. 6.5 presents the appropriate classical elimination tree.

Figure 6.5: Tridiagonal matrix and classical elimination tree

Unfortunately, the classical elimination cannot be parallelized.