Thread: Contraction mapping iterations

contraction mapping
phi x=((x^2)-2x+5)/4 with phi restricted to [0,2]

set up an iterative scheme with x0=1/2. give estimate on the maximum number of iterations needed to approach fixed point with error of less than 10^(-k) for any integer k??

Originally Posted by TS1

contraction mapping
phi x=((x^2)-2x+5)/4 with phi restricted to [0,2]

set up an iterative scheme with x0=1/2. give estimate on the maximum number of iterations needed to approach fixed point with error of less than 10^(-k) for any integer k??

A "fixed point" for phi is x such that . That is the same as or so . Try that as an "iterative scheme".