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1d
reviewed Approve Upper bound for a convex fractional function
2d
comment An upper bound for a function
Thanks, very elegant approach. Got me to the solution first, though the approach of the others is a bit more direct.
2d
accepted An upper bound for a function
2d
comment An upper bound for a function
Great answer! Took me a while to see the steps but now it's incredibly simple. Nice!
2d
revised An upper bound for a function
deleted 6 characters in body
2d
asked An upper bound for a function
2d
accepted How to find solutions for this nonlinear equation?
2d
comment Conditions for a unique root of a fifth degree polynomial
Thank you, I did not know this technique. Very elegant! It is possible to find sufficient conditions in terms of the coefficients using the Sturm sequences, although the polynomial long division makes it a lot of work and the resulting conditions are not particularly easy to work with. Then again, this is a 5th degree polynomial, so any uniqueness condition is likely not very simple.
2d
answered Cost per pound savings analysis between two data sets
Aug
24
comment Conditions for a unique root of a fifth degree polynomial
Yes that's what I thought. Doesn't even require the type of the critical points; just graphing them and connecting the dots will tell how many solutions there are. Still, I was hoping there was a simpler way, say a condition on the coefficients, since determining the solutions of a fourth degree polynomial is not a walk in the park either.
Aug
23
comment Conditions for a unique root of a fifth degree polynomial
Counts as one. I think of it as the number of solutions after removing duplicates.
Aug
23
asked Conditions for a unique root of a fifth degree polynomial
Aug
15
comment How to find solutions for this nonlinear equation?
Great, now I understand! So this is how I would approximate for small values of the parameters. For large values, I guess I just use, say, $r=1/\epsilon$. I leave the question open for now, maybe there is another idea, but your approach is very interesting and useful for many parameter values. Thanks.
Aug
14
comment How to find solutions for this nonlinear equation?
I see! You approximate $x$ with a series of $\epsilon$s, substitute it in the polynomial, and then match coefficients. Interesting! The $\epsilon$s need to be small so that higher order terms are not as important. But I don't quite understand why that requires $r,t,u$ to be small and not $e$?
Aug
14
comment How to find solutions for this nonlinear equation?
Thanks for clarifying the 5th degree polynomail issue, I suspected as much! Typically $|r|$ will not be small, but it is still interesting to see if assuming small $|r|$ allows to obtain workable solutions.
Aug
14
comment How to find solutions for this nonlinear equation?
Can you elaborate a bit on the steps you took or give a source where the approach is explained? It looks as if you assumed $r,t,u$ are small, which allows you to write a Taylor series for the entire term, but then how do you solve this series for $x$? I may be wrong though..;)
Aug
14
asked How to find solutions for this nonlinear equation?
Aug
11
reviewed Approve Calculating Rotation from centroid
Aug
11
revised Conditional variance of sum of two correlated random variables
deleted 1 character in body
Aug
11
reviewed Edit Limit of this sequence.