Partial Diagonalisation

Often only a fraction of the eigenvalues are required, sometimes only the largest or smallest. Generally if more than 10% are required there is nothing to be gained by not calculating all of them, as the algorithms for partial diagonalisation are much less efficient per eigenvalue than those for full diagonalisation. Routines are available to calculate the $M$ largest or smallest eigenvalues and also all eigenvalues in a particular range.