Joint Approximate Partial Diagonalization of Large Matrices
<|reference_start|>Joint Approximate Partial Diagonalization of Large Matrices: Given a set of $p$ symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these $p$ matrices is as close as possible to a diagonal matrix. We argue that when the matrices are of large dimension, then the natural generalization of this problem is to seek an orthonormal basis of a certain subspace that is a near eigenspace for all the matrices in the set. We refer to this as the problem of ``partial joint diagonalization of matrices.'' The approach proposed first finds this approximate common near eigenspace and then proceeds to a joint diagonalization of the restrictions of the input matrices in this subspace. A few solution methods for this problem are proposed and illustrations of its potential applications are provided.<|reference_end|>
@article{seghouane2024joint,
    title={Joint Approximate Partial Diagonalization of Large Matrices},
    author={Abd-Krim Seghouane and Yousef Saad},
    journal={arXiv preprint arXiv:2409.02005},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.02005},
    primaryClass={math.NA cs.NA}
}