Hey guys, can any of you shed any light on this strange looking example?!

The iteration Xn Xn+1 is given by:

Xn+1 = Xn + Xn(1 - A Xn)

A is an invertible mxm matrix and also :

ll1 - AXoll = q < 1.

Show that the sequence converges to A⁻1 with the estimates:
llXn – A-1ll < 1/(1-q) . llX0ll . ll1 – AXnll < 1/(1-q) . llX0ll . q(2^n)

Consider using matrix Rn = 1 - AXn and expressing A⁻1 in terms of Ro.


Help would be very much apprieciated and your knowledge is of great value to me.
May thanks!