The trend of more and more execution units can be expected to continue. Linear algebra algorithms typically exhibit good weak scaling behaviour, i.e. they scale to a larger execution unit count if the problem is also scaled. However, in many cases, the problem size is fixed. In that case additional execution units cannot be harnessed efficiently. Given a fixed problem size, the algorithm should scale while adding more and more execution units. This project addresses these cases; it attempts to design algorithms in such a way that they exhibit strong scaling behaviour.