Algorithms for the unitary eigenvalue problem
Roden Jason A. David · 2007
Eigenvalues of unitary matrices arise in a variety of contexts in applied mathematics. This dissertation present four new algorithms for computing the eigenvalues of unitary matrices. In chapter 1, we give an overview these algorithms, and then survey the major applications where eigenvalues of unitary matrices arise. In chapter 2, we present the unitary QR algorithm, an algorithm that can used to compute all of the eigenvalues of a unitary matrix. In chapter 3, we present two Krylov space algorithms that approximate some of the eigenvalues of a large unitary matrix. Finally, in chapter 4, we present an algorithm that compute the eigenvalues of a unitary matrix U when U is expressed as a product U = U1 Un of unitary matrices of the same order. As a special case, we consider the generalized eigenvalue problem for unitary matrices.