Real Fast Structure-Preserving Algorithm for Eigenproblem of Complex Hermitian Matrices

Abstract EN

It is well known that the flops for complex operations are usually 4 times of real cases.

In the paper, using real operations instead of complex, a real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices is given.

We make use of the real symmetric and skew-Hamiltonian structure transformed by Wilkinson's way, focus on symplectic orthogonal similarity transformations and their structure-preserving property, and then reduce it into a two-by-two block tridiagonal symmetric matrix.

Finally a real algorithm can be quickly obtained for eigenvalue problems of the original Hermitian matrix.

Numerical experiments show that the fast algorithm can solve real complex Hermitian matrix efficiently, stably, and with high precision.