An affine iterative system has the form u(k+1) = T u(k) + b. u(0) = c.
(a) Under what conditions does the system have an equilibrium solution u(k) = u*?
(b) In such cases, find a formula for the general solution. Look at v(k) = u(k) - u*.
(c) Solve the following affine iterative systems:
(i)

(ii)

(iii)

(iv)

(d) Discuss what happens in cases when there is no fixed point, assuming that T is complete.

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