A new method for the solution of eigenvalue problems

One among the class of iterations proposed by Osborne and Michaelson (1964) is discussed. It is shown that for the ordinary eigenvalue problem this iteration is of third order, and that it may readily be modified to be of third order for the general eigenvalue problem provided the eigenvalue parameter occurs linearly. The analysis also suggests a further modification which gives a third-order iteration for the non-linear problem.