The Q R algorithm with shifts of origin may be used to determine the eigenvalues of a band symmetric matrix A. The algorithm is described by the relations $$\matrix{ {{A_s} - {k_s}I = {Q_s}{R_s},} & {{R_s}{Q_s} = {A_{s + 1}}} & {(s = 1,2, \ldots )} \cr } $$ (1) where the Q s are orthogonal and the R s are upper triangular. It has been described in some detail by Wilkinson [5, pp. 557–561]. An essential feature is that all the A s remain of band symmetric form and R s is also a band matrix, so that when the width of the band is small compared with the order of the A s , the volume of computation in each step is quite modest. If the shifts ks are appropriately chosen the off-diagonal elements in the last row and column tend rapidly to zero, thereby giving an eigenvalue.