Journal of Computational and Applied Mathematics vol:189 issue:1-2 pages:580-591
A real symmetric matrix of order n has a full set of orthogonal eigenvectors. The most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric structured one, i.e., tridiacronal Z matrices or semiseparable matrices. This step is accomplished in O(n(3)) operations. Once the latter symmetric structured matrix is available, its spectrum is computed in an iterative fashion by means of the QR method in O(n(2)) operations.