HP Prime crashes in Function and Graph 3D App.

[lyuka]

Hi Albert

As the HP Prime emulator crashes so offten, I'm getting tired of it.

(11-18-2020 12:12 PM)Albert Chan Wrote:  Off topics: Why did you change convergence check ?
q <= r should be (q < 1 and q <= r), to avoid false positives.

In short, I had some convergence problems.

-- off topic But I'm sorry it's getting longer --
Talking about the convergence, the condition check
(q < 1 and q <= r)
assume the convergence radius become smaller than 1.

However, in some convergence tests, the radius of convergence never fell below 1,
and sometimes stayed well above 9 for some very large complex inputs.

If the calculation numerically oscillates but the radius does not change in large value,
then the calculation converges within the accuracy of the calculator, but the program cannot finish the calculation.
And it happened, but unfortunately I lost the value of that special case.

Instead of using the iteration counter, I changed the initial radius to MAXREAL or Infinity to ensure that the calculation ends.

As long as using Halleys method or Householders method of order 4 with my approximation as the initial guess,
the convergence at the first stage is monotonous and I think a proof* is needed,
but no false positives occur. No false jumps to other branches than W0 will occur.

* a Proof -- I think it's necessary, but it's beyond my (complex analysis) capabilities.