On the convergence velocity of the modified method of successive approximations

The modified method of successive approximations is used to calculate characteristic number and corresponding eigenfunctions of a given linear completely continuous operator acting in a normed space. While the operator acts in a Gilbert space, the method converges as a geometrical progression with any small denominator. For certain operators we can execute steps of the method algorithm analytically. It allows us to separate the method error from the other ones and to estimate a posteriori the convergence velocity of the approximate results obtained by the method.