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Geoff Oxberry

 Discussion on question by Jack: Using…

Imported from a comment discussion on scicomp.stackexchange.co...
Geoff Oxberry
Sep 24, 2014 01:55
@Jack: Agreed with Kirill here: Stack Exchange isn't good for long questions with lots of discussion. Having lots of comments in the comment section will get flagged (like this one). In addition, it's generally frowned upon to post repeat questions that are variations of each other. Your posts aren't exactly the same, but they're not too far off, and posting too many more about integration in a short span will start triggering mods to close them. As for the discussion, it's better to have a discussion in a chat room than in the comments.
Geoff Oxberry
Sep 24, 2014 01:55
You may want to look at the suggestions in Method for numerical integration of difficult oscillatory integral.
 

 Discussion between Geoffrey Irving an…

Imported from a comment discussion on scicomp.stackexchange.co...
Geoff Oxberry
Aug 4, 2012 06:00
I think having an accepted answer is fine; no need to close the question.
Geoff Oxberry
Aug 4, 2012 06:00
I believe that; I think the paper also mentions a $\tilde{O}(n)$ algorithm for finding the eigenvalues of those matrices. The main obstacle is the characteristic polynomial. Find that in $\tilde{O}(n)$, and you have your $\tilde{O}(n)$ algorithm. I'd be interested to see what the source the STOC paper cites has to say about the proof of the lower bound (which is apparently an exercise).
Geoff Oxberry
Aug 4, 2012 05:57
No problem!
Geoff Oxberry
Aug 4, 2012 05:49
@Geoffrey: Frobenius, block Frobenius, and tridiagonal matrices can all be specified using $O(n)$ data, so output data (at least at the end of that stage) is not an issue; rather, you need a fast way (i.e., $\tilde{O}(n)$ algorithm) to calculate the coefficients of the characteristic polynomial. Without the source, it's not immediately clear to me that the $\Omega(M(n))$ bound excludes that possibility, but the "fast algorithms" I've seen from searching around are all $\tilde{O}(n^{2})$. It's not a proof, but the evidence suggests that a $\tilde{O}(n)$ algorithm is unlikely.
Geoff Oxberry
Aug 4, 2012 05:49
@GeoffreyIrving: Let me clarify, then, with an edit.
Geoff Oxberry
Aug 4, 2012 05:49
@GeoffreyIrving: I think we're talking about different meanings of "nearly optimal". I am referring to that phrase when used in page 4 of the article, (re: stage (a)) "All of these algorithms are performed at nearly optimal cost of $O(M(n) \log(n))$ ops...", where $M(n)$ is the cost of a matrix-matrix multiply. If you can accomplish stage (b) in a matrix-free way, you can potentially get around the $\Omega(n^{2})$ bound on matrix-matrix multiplication. I know that LU decomposition and matrix-matrix multiply have the same complexity, but I don't know if that's true of individual linear solves.
Geoff Oxberry
Aug 4, 2012 05:49
@GeoffreyIrving: Look at Section 1.2 of the paper, where they separate the problem into three stages, (a) through (c). Calculating the eigenvalues is equivalent to solving stages (a) and (b); Section 1.2 gives the computational complexity of each stage, which is what I used to write my answer.
 

 Computational Science

General discussion for scicomp.stackexchange.com
Geoff Oxberry
Apr 8, 2012 18:18
@Nunoxic Condition numbers can be arbitrarily high. For examples of matrices with high condition numbers, you may want to look at Hilbert matrices. In general, something that's "ill-conditioned" probably has a condition number of at least 1e6 to 1e8.
Geoff Oxberry
Mar 23, 2012 00:42
@Nunoxic Aside from the Fortran linear algebra question on scicomp, I don't know of any such papers. Jack or Jed might know. I wouldn't think there would be a huge difference.
Geoff Oxberry
Mar 18, 2012 15:27
@AronAhmadia I answered that optimization question, because listening to those other answers, especially the top-voted one by the 65.3k rep user, could've backfired badly.
Geoff Oxberry
Mar 18, 2012 01:05
@AronAhmadia Is Madagascar really that bad?
Geoff Oxberry
Mar 17, 2012 23:29
@AronAhmadia I looked at the answers to that optimization question, and I just couldn't believe the advice.
Geoff Oxberry
Feb 28, 2012 15:00
Maybe. In any case, I cc-ed you on the long conversation I had with him here.
Geoff Oxberry
Feb 28, 2012 14:52
Agreed.
Geoff Oxberry
Feb 28, 2012 14:50
Yeah, I wish that question were clearer, as well as shorter. I think it's useful, but I feel like the actual question is buried in a statement
Geoff Oxberry
Feb 28, 2012 14:48
@AronAhmadia Are we talking about Faheem's question?
Geoff Oxberry
Feb 28, 2012 01:28
I have other obligations to attend to. My point is, please be constructive when you express opinions about the site and the actions of others. Have a good day!
Geoff Oxberry
Feb 28, 2012 01:26
@hhh: Typically, it would be $i, j, k = 1, \ldots , n$
Geoff Oxberry
Feb 28, 2012 01:25
@hhh: I'll post the common notation that makes it explicit.
Geoff Oxberry
Feb 28, 2012 01:25
@hhh: From what I read of your comments, I understood that you thought someone was manipulating the site. You're entitled to say that in your own Meta post, constructively.
Geoff Oxberry
Feb 28, 2012 01:23
I cleaned up the notation slightly.
Geoff Oxberry
Feb 28, 2012 01:23
Typically, in optimization problems, indices are assumed to be natural numbers.
Geoff Oxberry
Feb 28, 2012 01:19
@hhh: Yeah, that looks much better.
Geoff Oxberry
Feb 28, 2012 01:14
(cc: @@AronAhmadia for reference)
Geoff Oxberry
Feb 28, 2012 01:13
You obviously have a lot of passion for the site; I'd prefer it be channeled in a constructive way.
Geoff Oxberry
Feb 28, 2012 01:12
In the future, comments like that will be cause for a 7-day suspension, because they violate the terms of service of the site.
Geoff Oxberry
Feb 28, 2012 01:10
Anyway, I need to get back to doing research, so one final thing: the posts you've been writing recently (specifically many of the comments) have been inflammatory, verging on abusive. I was going to write you a mod message to that effect, but since we're here talking, calling a mod "evil" and comparing the site to Animal Farm is inappropriate.
Geoff Oxberry
Feb 28, 2012 01:07
I agree that it's hard to read.
Geoff Oxberry
Feb 28, 2012 01:07
You could still reformat the question.
Geoff Oxberry
Feb 28, 2012 01:03
This question was relatively simple to state, but not trivial by any means.
Geoff Oxberry
Feb 28, 2012 01:03
6
Q: Constraints involving $\max$ in a linear program?

N21Is there a straightforward way to formulate the following as a linear program, or something similarly amenable to easy solution? The problem is: minimize $A \;\mathrm{vec}(U)$ over symmetric $n\times n$ matrices $U$ subject to $U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}$ for all $i,j,k$. H...

optimization linear-programming
Geoff Oxberry
Feb 28, 2012 01:03
Simple can be good. I think it's possible to find simple questions that are nontrivial.
Geoff Oxberry
Feb 28, 2012 00:59
Another metric would be views.
Geoff Oxberry
Feb 28, 2012 00:59
Even then, I'd encourage you to ask questions that are nontrivial and interesting to people, since we need high quality questions on the site. It's something that you've mentioned a lot in your posts, and one metric for quality (though imperfect) is the question score (in votes).
Geoff Oxberry
Feb 28, 2012 00:56
You've also asked questions about optimization on Math.SE; that's another potential topic for questions on SciComp.
Geoff Oxberry
Feb 28, 2012 00:56
Surely you have problems that are in computational science. Numerical solution of ordinary differential equations, perhaps? You talked about the Euler method, for instance, but you could ask a different question on numerical integration, perhaps exploring a different issue than just asking if you reproduced the formula correctly.
Geoff Oxberry
Feb 28, 2012 00:53
I encourage you to come up with different ways of doing that. Variety would be a good start. Ask about technical problems that you face in computational science that aren't just symbolic manipulation.
Geoff Oxberry
Feb 28, 2012 00:52
I think that's a good point, and I think if you can find a constructive way to bring computational topics from Math.SE here, then you will have made an outstanding contribution to SciComp.
Geoff Oxberry
Feb 28, 2012 00:49
And people on SciComp still tried to help by offering you software recommendations.
Geoff Oxberry
Feb 28, 2012 00:48
Looking at the questions you ask on Math.SE, there's a lot more variety.
Geoff Oxberry
Feb 28, 2012 00:45
It's fine to answer your own question, but I think your question would have been downvoted anyway because it's too derivative. It's much like your other questions about symbolic manipulation.
Geoff Oxberry
Feb 28, 2012 00:43
So by the time you get to differential equations, people have caught on. Plus, it looks awfully similar to a question you asked about symbolic manipulation of differential equations on February 14.
Geoff Oxberry
Feb 28, 2012 00:41
And they realized that you had asked a similar question the very next day. In fact, Mark Booth mentions it in his comment.
Geoff Oxberry
Feb 28, 2012 00:41
2
Q: Power series approximation for any function such as $-e^{x^{2}}$ in some easily-accessed open-source software?

hhhMy comrades repeatedly encourages monotonous problems where the issue is the same: chain-rule and some basic arithmetic. Is there some computational way to derive power series approximations? Suppose I plug in some function such as $e^{x^{2}+x+ln(x)+x^{777}}$, $e^{x^2}$ or $x^{777}-ln(x)+e^{2x+1}...

software education
Geoff Oxberry
Feb 28, 2012 00:41
But then people took a look and saw your slightly earlier question:
Geoff Oxberry
Feb 28, 2012 00:41
And it's a good question. We needed a question that talked about how to deal with pencil and paper problems, because symbolic manipulation can be important in deriving formulas that are part of algorithms in computational science.
Geoff Oxberry
Feb 28, 2012 00:39
10
Q: Is there any open-source or easy-to-access software that can simplify algebraic expressions like $x^{2}+2x+3, x=\sqrt{2}t-1$?

hhhI always calculate things by hand, but now my comrades are getting nasty and making a lot of repetitive exercises involving just plugging things in like the expression above. I am particularly interested in open-source software such as Python or R to simplify these kinds of equations. I tried usi...

education symbolic-computation
Geoff Oxberry
Feb 28, 2012 00:39
Virtually everyone posted links to software packages and source code for this question of yours: