Timeline for Can you recommend an efficient method for finding the least integer satisfying my inequality?
Current License: CC BY-SA 3.0
15 events
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| Jan 7, 2013 at 20:57 | comment | added | Artes | @Silvia Thanks, complete answers would deserve a bounty. | |
| Jan 7, 2013 at 19:55 | comment | added | Silvia | @Artes Hmm.. They are really challenging, and interesting. You got my +1s :) | |
| Jan 7, 2013 at 19:42 | comment | added | Artes | @Silvia Since the OP is pleased with the answers, discussing reliable automatic methods for $k \leq 1000$ would be an overkill. Nonetheless I like more challenging questions even though e.g. I still haven't accepted answers to my questions mathematica.stackexchange.com/users/184/artes?tab=questions | |
| Jan 7, 2013 at 19:30 | comment | added | Silvia | @Artes Thanks. I agree with you that none of the present answers are complete. But a similar question with $n\sim 1000$ would, in my opinion, be a bit nontrivial for automatic methods. (In fact I'd expect to see it in site like Project Euler.) In general it looks like an interesting problem. | |
| Jan 7, 2013 at 19:12 | comment | added | Artes |
@Silvia I like FindMinimum[..., Method -> "PrincipalAxis"], This seems to work well for $n(25)$. Nevertheless I'm not pleased with it e.g. for $n(30)$. Neither my method is straightforward, but seems to be indispensable for finding the exact value which I found to be 32322783001133. I would like someone to ask a question like this to find an automatic method for any $n(k)$ for e.g. $k \leq 1000$. That would be a really good question. Even this one is nice. I don't think any of the present answers are complete. Nonetheless +1.
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| Jan 7, 2013 at 18:06 | comment | added | Silvia | @Artes I see. I was thinking those options will remarkably increase the evaluation time before. Thanks for your reminding and please see my edit. | |
| Jan 7, 2013 at 18:02 | history | edited | Silvia | CC BY-SA 3.0 |
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| Dec 31, 2012 at 9:31 | vote | accept | chyanog | ||
| Dec 31, 2012 at 9:31 | vote | accept | chyanog | ||
| Dec 31, 2012 at 9:31 | |||||
| Dec 31, 2012 at 2:15 | comment | added | Artes |
@Silvia I mean that in order to have more reliable results one has to use options in NSum like AccuracyGoal, NSumTerms etc. Here you should include e.g. possible options of the function myfunc.
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| Dec 31, 2012 at 1:55 | comment | added | Silvia |
@Artes hmm let me have a think.. The key point of adopting "PrincipalAxis" is to use the built-in root-searching routine for automatic "trial and error". I'm thinking of defining a proper custom merit function so it can compute fast and precision, but I'm currently in travel and don't have access to an MMA..
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| Dec 29, 2012 at 13:14 | comment | added | Silvia |
@Mr.Wizard Yes you're right. I nearly totally forgot Positive!
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| Dec 29, 2012 at 13:02 | comment | added | Mr.Wizard |
I believe you can replace the entire definition of myfunc with myfunc[n_?Positive] := NSum[1/(i + Sqrt[i]), {i, Round @ n}]
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| Dec 29, 2012 at 11:49 | history | edited | Silvia | CC BY-SA 3.0 |
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| Dec 29, 2012 at 11:43 | history | answered | Silvia | CC BY-SA 3.0 |