On the eigenproblem for orthogonal matrices
Gregory S. Ammar, William B. Gragg, Lothar Reichel · 1986
A numerically stable method, that uses the structure of the matrices, for computing the eigenvalues and eigenvectors of orthogonal matrices is described. The orthogonality of the matrices reduces the eigenproblem to three singular value problems for bidiagonal matrices, whose elements are explicitly known functions of the Schur parameters.