Timeline for Numerical differentiation. What is the best method?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2020 at 7:24 | comment | added | F. Jatpil | I am quite disappointed by the community, starting from journal referees up to this forum. My method is down-voted (why on Earth??), Benoît Kloeckner stops discussing at the point where he should start arguing, and you say misleading statements. I cannot prevent you from having subjective feelings and seeings but I see not real value in them. The most precise method is at least a theoretical concept which deserves its attention.And it is also practical I believe (maybe not for Diff. eq. on large grids). Concerning $x\pm h$ w.o. rounding errors I do not get it, maybe you can be more explicit. | |
| Jun 3, 2020 at 7:22 | comment | added | F. Jatpil | How it sounds to you A)maybe get 1 digit or 2,B)most probably increase precision by 2 or 3 orders.A) is what you say,B) is what tests say.Why are you making such completely misleading statements?Certainly not from what I did. I think you don’t like the method (why?) and simply say wrong things to make it look worse.Does this comply with scientific approach and honesty?And what about an alternative?Do you have one?If not then we can agree: the method is (it is!) the most precise one for ND now known in the most usual context of fixed machine epsilon for a general (e.g. non-analytic) function. | |
| May 28, 2020 at 13:56 | comment | added | oli | @F.Jatpil: In your linked paper the tables imply that if h is close to properly chosen for the specific method, then you get 1 or 2 digits at most of increased accuracy. In the case of central finite differences I expect this improvement to vanish if h is exactly properly chosen and rounding errors are avoided for (x+h) and (x-h). If you wanna argue that we can perturb floating arithmetic calculations several times, average the result, and maybe get one digit or two in accuracy, fine, that might often work. I don't see a real value in that. | |
| May 28, 2020 at 12:22 | comment | added | F. Jatpil | @oli. How do you increase precision if you download compiled numerical libraries, let’s say Java with double? Are you going to decompile them? Or reprogram java virtual machine? Well, there is no guarantee, because it is statistical, and in statistics nothing is guaranteed. But it is excellently working method with well funded justification which increases precision by orders of magnitudes in abs error. The original question does talk about imported libraries it does not talk about convergence rate. Please remind me: what is the alternative for downloaded compiled libraries? | |
| May 27, 2020 at 20:14 | comment | added | oli | From my point of view I can see why it is "systematically refused by journals". There is no guarantee that 'averaging out' rounding errors will yield better results, neither does this improve convergence order or similar. I can get reliably get higher accuracy by increasing my precision, with comparable increase of computational effort. | |
| May 20, 2018 at 21:34 | comment | added | F. Jatpil | You are wrong to say "strength" of the method. The question clearly says "precision" and this is discuddes here. As mentioned: one downloads numerical libraries he did not program and one wants the most precision when differentiating: it is a well defined problem. | |
| May 20, 2018 at 21:00 | comment | added | Benoît Kloeckner | "we discuss here precision and not time consumption" This makes no sense - the strength of a method is basically how much time is needed to achieve a given precision (except when memory complexity is the limiting factor, but I do not see a reason to expect this to be the case here). | |
| May 20, 2018 at 20:41 | history | edited | F. Jatpil | CC BY-SA 4.0 |
Changes made on request.
|
| May 18, 2018 at 9:35 | comment | added | Tommi | The answer would be vastly improved by giving a summary of the contents of the link. | |
| Jul 25, 2017 at 9:46 | review | Late answers | |||
| Jul 25, 2017 at 10:10 | |||||
| Jul 25, 2017 at 9:31 | review | First posts | |||
| Jul 25, 2017 at 9:33 | |||||
| Jul 25, 2017 at 9:28 | history | answered | F. Jatpil | CC BY-SA 3.0 |