Fast computation of eigenvalues of periodic CMV matrices
arXiv:2607.064008.6
Predicted impact top 11% in NA · last 90 daysOriginality Incremental advance
AI Analysis
This provides a more efficient algorithm for computing eigenvalues of periodic CMV matrices, which are important in certain mathematical and physical contexts.
The paper presents a fast method for computing eigenvalues of periodic CMV matrices in O(n²) time using O(n) data, compared to standard O(n³) time with O(n²) data.
Periodic CMV matrices are unitary matrices that can be specified by $O(n)$ data. Their eigenvalues can be computed by standard methods, storing them as conventional matrices (using $O(n^{2})$ data) in $O(n^{3})$ time. Here a fast method that computes the eigenvalues in $O(n^{2})$ time (using $O(n)$ data) is presented.