Timeline for Current Research in Numeric Mathematics
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2021 at 14:41 | history | edited | Stefan Kohl♦ |
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| Apr 18, 2021 at 1:33 | comment | added | Rodrigo de Azevedo | IMHO, calculations with unlimited precision can still be numerical. To me, it seems that numerical algorithms are designed for an ideal real RAM computer, and since that ideal does not exist, one makes do with floating-point values. One could also make do with arbitrary-precision rationals, provided that the expected number of iterations is small — say, about $10$. It could work for Newton's method, but it would be a disaster for numerical integration of ODEs. | |
| Oct 15, 2016 at 15:44 | comment | added | user2277550 | Arent there many cases where you can prove that symbolic closed forms are not available? Differential galois and such stuff. At least over there we need numerical computation. | |
| Sep 14, 2015 at 17:39 | answer | added | David Ketcheson | timeline score: 9 | |
| Sep 13, 2015 at 19:00 | comment | added | Timothy Chow | For a specific example where you might naively think that exact computation is used, consider integer linear programming. This is a purely combinatorial problem and "on paper" is most naturally solved using exact integer arithmetic. But in practice, all the best implementations (such as CPLEX) use floating-point computations, because exact integer arithmetic is much slower. | |
| Sep 13, 2015 at 18:57 | comment | added | Timothy Chow | Ironically, it is because of, rather than despite, increasing computational power that fast approximate algorithms are increasing in importance. In the early days, the boundary between computable and uncomputable was the interesting one. As computers became better, interest shifted to the boundary between P and NP. Nowadays, linear and sublinear-time algorithms are all the rage. The more powerful our computers, the more data we amass, and the less we can afford to carry out exact computations. | |
| Sep 13, 2015 at 14:04 | answer | added | Thomas Klimpel | timeline score: 12 | |
| Sep 13, 2015 at 13:55 | vote | accept | Manfred Weis | ||
| Sep 13, 2015 at 13:54 | comment | added | Manfred Weis | @Suvrit of course numeric mathematics is important for all calculations with finite precision that are related to "classical" problems like finding zeros, integration, solving differential equations and so my question aimed at research in numeric mathematics and new problems that demand new numeric methods. Federico Poloni has convincingly pointed out the ongoing importance of research in numeric methods despite the boost in computational power. | |
| Sep 13, 2015 at 13:44 | comment | added | Suvrit | Wow, "should have lost its importance" is the exact opposite of the conclusion that I would have arrived at given that pretty much nothing is left untouched by computing! | |
| Sep 13, 2015 at 13:09 | comment | added | Thomas Klimpel | scicomp.stackexchange.com | |
| Sep 13, 2015 at 12:43 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Sep 13, 2015 at 11:40 | comment | added | Beni Bogosel | quora.com/… | |
| Sep 13, 2015 at 11:08 | answer | added | Federico Poloni | timeline score: 37 | |
| Sep 13, 2015 at 10:40 | history | asked | Manfred Weis | CC BY-SA 3.0 |