A Randomized Algorithm for Simultaneously Diagonalizing Symmetric Matrices by Congruence
The paper introduces a randomized simultaneous diagonalization by congruence (RSDC) algorithm that reduces the problem to a generalized eigenvalue problem using two random linear combinations. It proves exact recovery with probability one for exactly SDC families and provides perturbation bounds for regular SDC families, including a high‑probability robust‑recovery guarantee under a positive definiteness assumption. The method is combined with an optimization algorithm and tested on synthetic data, image separation, and EEG analysis, outperforming existing optimization‑based methods in effici…
Source: OpenAlex