Determination of the eigenvalues and eigenvectors of a matrix is important in many areas of science, for example in web ranking [8, 15], computer graphics and visualization [24], quantum mechanics [5], statistics [12, 20], medicine, communications, construction vibration analysis [3, 23]. One of the most important numerical methods designed to calculate the eigenvalues and eigenvectors of matri...

For a self-adjoint linear operator with discrete spectrum or a Hermitian matrix the “extreme” eigenvalues define the boundaries of clusters in the spectrum of real eigenvalues. The outer extreme ones are the largest and the smallest eigenvalues. If there are extended intervals in the spectrum in which no eigenvalues are present, the eigenvalues bounding these gaps are the inner extreme eigenval...