PLSSVM is a library that enables the efficient training and execution of Support Vector Machines, which can be used to classify data. It does so by utilizing various high performance computing frameworks to construct and solve a system of linear equations. The conjugate gradient algorithm is used to iteratively solve this linear system. Large datasets with many features, resulting in ill-conditioned kernel matrices have a negative impact on the convergence of the CG method.

To remedy this problem, the goal of this thesis is to analyze different preconditioners in the context of the preconditioned conjugate gradient algorithm, in order to reduce the condition number of the linear system, leading to better convergence and higher stability in regards to different hyperparameter sets.

To achieve this goal three different preconditioners were implemented with SYCL and tested, showing that the usage of a preconditioners can indeed help to improve the mentioned aspects, resulting in fewer iterations (up to 78\%) to converge and enabling the usage of hyperparameter combinations that were not possible before.