I have the following problem. My alpha must be between {0,1}. The function is
f[x_] = Log[x] + x - 0.5;
y[x_] = x - alpha*f[x]/f'[x];
0.75 + 4 (y[0.75] - 0.75) f[0.75]/(3 f[0.75] - 2 f[y[0.75]])
I should make a loop with all the values between 0 and 1 until the end result no longer change - it must happen automatic. I have tried with while, do and fixed point, but I did not get any result. I should get for Alpha = 0.5046 and for end result 0.766249. Thanks in advance
