Loop with definite scope of alpha until the result no longer change?

Questions
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1

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

2

Please make sure you know how to format code properly: https://wolfr.am/READ-1ST

I have tried with while, do and fixed point, but I did not get the right result.

Please edit your post and add code you have tried as you mention above.

3

You may try this:

f[x_] := Log[x] + x - 0.5
y[x_] := x - \[Alpha] f[x]/f'[x]

Table[FixedPointList[# + (4 (y[#] - #) f[#])/(3 f[#] - 2 f[y[#]]) &, 0.75],{\[Alpha], 0, 1, 0.01}]
4

That is what i need. Thank you a lot. Can you tell me how to display the current value of alpha and the relevant result.

5

Sure, you can apply FixedPoint[] as well as FixedPointList[]:

f[x_] := Log[x] + x - 0.5
y[x_] := x - \[Alpha] f[x]/f'[x]

Table[Print["\[Alpha] = ", \[Alpha], " ", 
  FixedPoint[# + (4 (y[#] - #) f[#])/(3 f[#] - 2 f[y[#]]) &, 
   0.75]], {\[Alpha], 0, 1, 0.01}]
6

Thank you very much! You save me. Have a nice day :slight_smile: