Timeline for Mathematica accuracy errors when creating data
Current License: CC BY-SA 4.0
8 events
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| Aug 20, 2021 at 17:24 | comment | added | Gabi23 | Let us continue this discussion in chat. | |
| Aug 20, 2021 at 16:27 | comment | added | Michael E2 |
What causes the messages is AccuracyGoal being higher than the working precision can handle. The setting I suggested lowers it to the best, achievable accuracy possible at machine precision (and you might need to lower it, not raise it, a little more, since it's an approximation). PrecisionGoal should not be set higher than the working precision and probably should be a little less, since it's impossible to avoid roundoff error. You might look up arbitrary and machine precision numbers in Numbers if you don't know about them.
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| Aug 20, 2021 at 16:14 | comment | added | Gabi23 | @MichaelE2 Thank you, I will give that a try. Maybe I should also manually set PrecisionGoal and AccuracyGoal to higher numbers like 16 too. | |
| Aug 20, 2021 at 16:04 | comment | added | Michael E2 |
...where deriv = D[RiemannSiegelTheta[t], t]
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| Aug 20, 2021 at 16:02 | comment | added | Michael E2 |
FindRoot is giving the best answer possible at machine precision for grampoint[65]. You can check consecutive floating-point values for t this way: Block[{n = 65}, RiemannSiegelTheta[grampoint[n] {1 - $MachineEpsilon, 1, 1 + $MachineEpsilon}] - (10^12 + n - 1) Pi]. If that solution is unsatisfactory, then you should set WorkingPrecision to a number, perhaps, WorkingPrecision -> 16 or higher. (Can't get a better machine-precision result this way, tho.) If machine precision is satisfactory, try setting AccuracyGoal -> -Log10[(t*deriv /. t -> zeros[[5000]]) $MachineEpsilon]
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| Aug 20, 2021 at 15:53 | history | edited | Gabi23 | CC BY-SA 4.0 |
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| Aug 20, 2021 at 15:48 | history | edited | Gabi23 | CC BY-SA 4.0 |
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| Aug 20, 2021 at 15:23 | history | asked | Gabi23 | CC BY-SA 4.0 |