Computational Complexity of Diagonalization and Related Procedures

Investigate and resolve fundamental open questions about the computational complexity of matrix diagonalization and related procedures (e.g., orthogonal diagonalization of real symmetric matrices) under realistic bit complexity models, aiming to clarify algorithmic limits and develop efficient methods.

Background

The paper’s main algorithm assumes access to diagonalization routines and discusses how to implement the method with approximate diagonalization oracles in realistic computational models. The authors note broader unresolved issues around the complexity of diagonalization and related tasks.

Understanding these complexity questions is important for the bit-complexity analysis of algorithms that depend on spectral computations, including those for probabilistic distance estimation.