- #1
Scootertaj
- 97
- 0
Homework Statement
Consider the system
x = [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x+y)^2}[/itex] - 2/3
y = x = [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x-y)^2}[/itex] - 2/3
Find a region D in the x,y-plane for which a fixed point iteration
xn+1 = [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x_n + y_n)^2}[/itex] - 2/3
yn+1 = [itex]\frac{1}{\sqrt{2}}[/itex] * [itex]\sqrt{1+(x_n - y_n)^2}[/itex] - 2/3
is guaranteed to converge to a unique solution for any (x0,y0)[itex]\in[/itex]D
a) State clearly what properties this region must have
b) find a region with these properties and show it has these properties
Homework Equations
Seen above
The Attempt at a Solution
Not really sure where to start.
I don't know, in general, what properties are required.