The application of this method to Hermitian matrices is essentially based on the Sturm sequence property, which means that for any given real number [lambda], the number of sign changes in the sequence of the characteristic polynomials of the principal leading submatrices of an N x N Hermitian matrix A equals the number of eigenvalues which are less than that [lambda].
To this end, we use the Sturm sequence property of the polynomials (2.
Compute the the ratios of consecutive pairs of Sturm sequence of polynomials (2.
Find the number of sign changes in the Sturm sequence of polynomials (2.
1 for finding the number v of sign changes in the Sturm sequence.