Abstract: In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.
Abstract: In this paper we introduce an efficient solution
method for the Eigen-decomposition of bisymmetric and per
symmetric matrices of symmetric structures. Here we decompose
adjacency and Laplacian matrices of symmetric structures to submatrices
with low dimension for fast and easy calculation of
eigenvalues and eigenvectors. Examples are included to show the
efficiency of the method.