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…
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…
Efficient joint diagonalization techniques like RSDC can support Swiss AI research in signal processing, data analysis, and related machine‑learning applications.
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