1
$\begingroup$

I want to draw the error of the two iterative methods.

ListPlot@Block[{$MinPrecision = 50, $MaxPrecision = 50}, 
  Log[Table[
    Abs[Nest[Power[# + 1, (3)^-1] &, 1., i] - 
      Root[#^3 - # - 1 &, 1]], {i, 1, 10, 1}]]]
ListPlot@Block[{$MinPrecision = 50, $MaxPrecision = 50}, 
  Log[Table[
    Abs[Nest[(2 #^3 + 1)/(3 #^2 - 1) &, 1., i] - 
      Root[#^3 - # - 1 &, 1]], {i, 1, 10, 1}]]]

However, the accuracy of the second iteration method is not enough to draw the parabola completely.

enter image description here

What can I do to improve the accuracy of drawing and get the correct scatter plot?

$\endgroup$

1 Answer 1

1
$\begingroup$
  1. Don't start with machine precision.

  2. Increase precision.

.

ListPlot@Block[{$MinPrecision = 1000, $MaxPrecision = 1000}, 
  Log[Table[
    Abs[Nest[(2 #^3 + 1)/(3 #^2 - 1) &, 1.`1000, i] - 
      Root[#^3 - # - 1 &, 1]], {i, 1, 10, 1}]]]
$\endgroup$
1

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.