A Jacobi-like algorithm for normal matrices by the skew-symmetric part
This work provides a more efficient algorithm for eigenvalue computation of normal matrices, particularly beneficial for applications in statistics on manifolds.
The paper presents a fast Jacobi-like algorithm for computing eigenvalues and eigenvectors of real normal matrices, leveraging Paardekooper's method for skew-symmetric matrices. It is faster than other Jacobi-like algorithms for matrices with mostly complex eigenvalues, such as random orthogonal matrices.
We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The method is most efficient for matrices where most eigenvalues are complex, such as random orthogonal matrices arising in the context of statistics on manifolds. In this case, the method is faster than the other Jacobi-like algorithms. In the last section of this paper, we also give explicit formulas for the nearest symmetric skew-Hamiltonian and the nearest ortho-symplectic matrix. These problems arise in the design and the analysis of the algorithm.