- #1
Scootertaj
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1. The problem statement:
In what region can we choose x0 and get convergence to the root x = 0 for f(x) = e-1/x^2
xn+1 = xn - f(xn) / f'(xn)
The only thing I've come across is a formula that says |root - initial point| < 1/M where M = max|f''(x)|/(2min|f'(x)| where x belongs to a "sufficiently small interval"
My thought: [-1,1]
In what region can we choose x0 and get convergence to the root x = 0 for f(x) = e-1/x^2
Homework Equations
xn+1 = xn - f(xn) / f'(xn)
The Attempt at a Solution
The only thing I've come across is a formula that says |root - initial point| < 1/M where M = max|f''(x)|/(2min|f'(x)| where x belongs to a "sufficiently small interval"
My thought: [-1,1]