On the convergence velocity of the modified method of successive approximations in generalized spectral problems

The modified method of successive approximations [1-3] is used to calculate characteristic numbers and corresponding eigenfunctions of a given linear completely continuous operator acting in a normalized space. While the operator acts in a Gilbert space, the method converges as a geometrical progression with any small denominator [4]. The method was expanded on spectrum problems with polynomial operator pencils in [5, 6]. In this article it is shown that the convergence velocity of a operator pencil eigenvalues calculated by the method has the same properties as in a linear case.