This thesis investigates the potential of solving large-scale linear systems of equations (LSEs) in the Tensor Train (TT) format. First, we study when this approach can outperform traditional solvers like Conjugate Gradient (CG) and Gaussian Elimination (GE). In turn, we examine the time complexity of the TT-solve technique when applied to ill-conditioned, sparse, and symmetric positive definite (SPD) matrices. This enables us to assess the scenarios where TT-solve may offer significant advantages.
During this exploration, we have also identified and proposed solutions for a handful of research gaps that could further optimize the TT-solve process. These include challenges related to poorly factorizing matrix sizes, as well as the need for a deeper understanding of the trade-offs between TT-matrix (TTM) rank and maximal mode size during the decomposition process. Additionally, the study examined the potential for altering the coefficient matrix through techniques like variable reordering and partial Gaussian elimination (PG) to achieve lower TTM-ranks without affecting the solution of the LSE.

Transitioning to use automated vehicles is a gradual process. Until full automation capabilities are developed there is a need to mediate which driving entity - human or autonomous driving system (ADS) - should be in control depending on the circumstances. This research aims at investigating the switching between manual and automated driving in semi-autonomous vehicles when the ADS becomes unfit to drive. To this end, a simple environment simulation was created and an MDP model was formulated that accounts for sensor failures and leaving the operational design domain (ODD). Deep Q-Network (DQN), a deep reinforcement learning (RL) algorithm was trained and evaluated against a hand-curated decision-tree-based standard. The DQN-based policy did not reach the performance of the baseline algorithm. The conclusion is drawn that using DQN to handle this multi-objective decision problem using an intuition-based reward function cannot learn an optimal policy.