Jacobi-Davidson type methods for computing rovibronic energy levels of triatomic molecules

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The stationary Schrödinger equation presents a significant challenge in various natural sciences, with explicit symbolic solutions being rare. Consequently, numerical techniques, particularly for giant Hermitian eigenvalue problems, are often employed. This thesis focuses on triatomic molecules exhibiting the Double-Renner effect. It begins by explaining the theoretical background of the Schrödinger problem and discusses methods for transitioning to finite-dimensional Hermitian matrices that approximate the original Hamiltonian, making it suitable for numerical analysis. However, conventional direct solvers, such as the QR method and RRR algorithm, face limitations due to high storage demands and lengthy computing times, which can extend to weeks. Thus, the main focus shifts to Jacobi-Davidson type methods, which are iterative projection algorithms. The goal is to demonstrate that these methods are more efficient in terms of computing time compared to direct eigensolvers and other iterative projection algorithms like Lanczos and Davidson. This involves constructing suitable preconditioners for shift-and-invert systems that leverage the specific problem's inherent information. Additionally, efficient routines for matrix-vector multiplication are crucial for success. The effectiveness of these approaches is supported by extensive numerical experiments and results.