I am a theoretical mathematician who works on the iterative method to find some generalized inverse of my interest. When I have tried some numerical example in Mathematica $11.0$, this does not converge to what I have proved theoretically. I have convinced myself to some extend that this is because of the rounding error when you use floating point arithmetic.
I need a proper explanation with the proper reference to justify this.
How does one theoretical mathematician should look into this and stop the discussion in his paper?
Thank you in advance.