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)llXn – A-1ll

A is an invertible mxm matrix and also :

ll1 - AXoll = q < 1.

Show that the sequence converges to A⁻1 with the estimates:

<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!