Madhavi Prakash Rose Hills
Deterministic Pseudospectral Shattering & Rank-Revealing Factorization
Eigenvalue problems are central to countless applications in engineering and the sciences, from analyzing vibrations in mechanical systems to understanding complex data. To avoid pathological cases and improve stability, many modern algorithms add small random perturbations to the input matrices—a technique known as pseudospectral shattering. This randomization helps to spread out clustered eigenvalues and improve the reliability of results. However, randomness introduces unpredictability, making results harder to verify or reproduce. This project asks a fundamental question: can we achieve the same stabilizing effect using deterministic techniques instead? Additionally, can near-optimal performance—comparable to fast matrix multiplication speeds—be ensured without relying on randomness? Any insights into these questions could have broader implications, extending to other randomized algorithms in numerical linear algebra and scientific computing.
Message To Sponsor
Thank you so much for providing me with the opportunity to pursue this project! I am extremely grateful for your generosity and am beyond excited to work with my mentors to contribute to the field of numerical linear algebra. This experience will allow me to deepen my understanding of algorithm design and grow as a researcher.