Rayleigh-schrödinger series for defective spectral elements of compact operators in banach spaces: Second Part: Numerical Comparison with Some Inexact Newton Methods

Numerical computation of Rayleigh-Schrödinger Series for maximal invariant sub-spaces is done for compact integral operators with defective eigenvalues. The series are applied to refine iteratively an approximate starting basis. The integral operators are discretized by different approximation methods which are known to be a strongly stable approximations at any nonzero eigenvalue. Rayleigh-Schrödinger Series are compared with three inexact Newton methods that perform the same goal.