Contraction mapping iterations

• Apr 17th 2010, 05:03 AM
TS1
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??
• Apr 17th 2010, 05:34 AM
HallsofIvy
Quote:

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 $\frac{x^2- 2x+ 5}{4}= x$. That is the same as $x^2- 2x+ 5= 4x$ or $6x= x^2+ 5$ so $x= \frac{x^2+ 5}{6}$. Try that as an "iterative scheme".