Talk:Numerical analysis

Link bugs

Why are some of the free links without apostrophes also closed to editing?

Apparently because there are newlines in them in the source --drj

So now Catastrophic loss of significance is fixed. rchase

Scientific computing

As far as I know, numerical analysis is nowdays called scientific computing. It seems natural to me to use the modern term rather than the old term. Should this article be moved/redirected to scientific computing? --DanielJanzon 15:22, 3 Nov 2004 (UTC)

You don't have to do any "computing" to do numerical analysis. Gershgorin discs fit under numerical analysis, but not necessarely under scientific computing. Loisel 17:00, 3 Nov 2004 (UTC)

Exactly, the theoretcial analysis side of it is separate, though closely related to the computing issue. - Taxman 18:17, Nov 3, 2004 (UTC)

Should scientific computing have it's own article? On my (Swedish) university (of Uppsala) all courses previosuly given in the field numerical analysis are now regarded as courses in "science of computing", which I assumed to be synonymous to the english term scientific computing. Do you guys know what you are talking about or do you just assume that numerical analysis is not fully contained in scientific computing because it doesn't sound like that listening to the term "scientific computing"? A search on Amazon seems (to me) to favor your view. Sorry for the rambling, --DanielJanzon 13:09, 4 Nov 2004 (UTC)

The words are interchangeable to a degree, but yes I do know what I'm talking about. I'm doing a postdoc at university of Geneva, more or less in scientific computing and numerical analysis. Loisel 14:25, 4 Nov 2004 (UTC)

I can confirm what Loisel says. Numerical analysis refers more to the theoretical side (for instance, the Gershgorin discs mentioned above) and scientific computing more to the practical side (for instance, MPI = Message Passing Interface), but there is a large overlap. Some people indeed use scientific computing in a broad sense to include all of numerical analysis, but other people use numerical analysis in a broad sense to include all of scientic computing. Ask some professors in Uppsala if you don't believe us. -- Jitse Niesen 15:44, 4 Nov 2004 (UTC)

Since "numerical metehods" (NM) redirects to "numerical analysis" (NA) I think "scientific computing" (SC) should do that also. To me, NM and SC seem very close to each other (closer than NA and SC). For instance Hamming writes in "Numerical Methods for Scientist and Engineers" p. 4 "Numerical analysis seems to be the study in depth of a few, somewhat arbitrarily selected, topics and is carried out in a formal mathematical way devoid of relevance to the real world. Numerical methods, on the other hand, try to meet the need for methods to cope with the potentially infinite variety of problems that can arise in practice". A bit frenzied, and maybe not very up-to-date, but I still believe SC should redirect to NA if NM does. Am I right? --DanielJanzon 19:33, 5 Nov 2004 (UTC)

Yes, I think so too. -- Jitse Niesen 23:11, 5 Nov 2004 (UTC)

I thought numerical analyis was essentially aimed at approximating continous mathematics. This is not obvious in the definition in the article. Someone competent in the matter might consider adding that to the article. --DanielJanzon 19:33, 5 Nov 2004 (UTC)

You're right. I think the article is generally not in a very good shape (I worked a bit on it myself, so hopefully nobody will take this personally), but I haven't found the energy to try and improve on it. Perhaps later. -- Jitse Niesen 23:11, 5 Nov 2004 (UTC)

Reversion of recent anonimous contributions

The recently added text has quite a bit of flaws:

First sentence is almost as a tautology, saying "numerical analysis is about numerical solutions". For now, the wording "numerical solution" is not defined, that will be dealt with later.
The wording "it deals with" shows up all the time.
The introductory paragraph went into way too much detail, it is meant to be a short overview.
The part in the ==General introduction== goes off to talk optimization, and again, goes into unnecesary detail for this stage.

As such, I found the contributions to be overall poor style, without adding much valuable, so I reverted the thing. Oleg Alexandrov 19:26, 31 July 2005 (UTC)[reply]

Moving the software out of the page

I moved the list of software out of the page, to a seperate article List of numerical analysis software. This is for several reasons.

First, the list was outgrowing the page. I felt that the article as losing it's main point as a science topic, and becoming an application topic. Second, it hindered the freedom to add rarely used software, which would be non-notable in the main article. Third, this way, we can add much information to the list of software, may be maintain it as a table (showing which platform they run on, licence, whether they are free/opensource, how large amounts of data they can handle etc.). I hope no one would oppose this move. Greenleaf 07:58, 9 September 2005 (UTC)[reply]

I think that shortening the software section in this article and moving most of it to a new article was a good idea. Thanks. Oleg Alexandrov 15:18, 9 September 2005 (UTC)[reply]

Inaccurate definition

"Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics) that do not have an explicit, direct solution." Gaussian elimination is one of the most prominent algorithms in numerical analysis. It has nothing to do with continuous mathematics and the solution is direct. That's just one example. I think that the inaccuracy can be characterized by the definition including only methods which suffer from truncation error. It neglects methods which suffer from only round-off error.

The definition is certainly not supposed to include only methods suffering from truncation error. Gaussian elimination solves Ax = b where x is a vector of reals. This is a problem in continuous mathematics (x is chosen from a continuum) and not in discrete mathematics. The phrase "that do not have an explicit, direct solution" serves to distinguish numerical analysis from symbolic mathematics. However, I agree that the word "direct" is ill-chosen since Gaussian elimination is called a "direct method" as opposed to an "iterative method" like Gauss-Seidel. Do you have a proposal for a better definition? -- Jitse Niesen (talk) 13:25, 29 November 2005 (UTC)[reply]

Would it work to substitute closed-form solution? Otherwise how about just removing the direct. Explicit already gets across part of the idea. - Taxman ^Talk 13:45, 29 November 2005 (UTC)[reply]

I thought about replacing it by "closed-form", but I fear that that is also open to misinterpretation: for instance, computing the sine is also part of numerical analysis, I think, but expressions like sin(1) are general considered to be closed form. I hadn't thought about just removing "direct". I like that, so I changed the definition, expecting that people who disagree will say so. -- Jitse Niesen (talk) 14:47, 29 November 2005 (UTC)[reply]

Yes, but in that sense the definition is wrong anyway, because numerical analysis includes evaluating polynomials which are clearly closed form. So perhaps it should say numerical analysis techniques are particularly valuable for evaluating problems where there are no closed form solutions, but the methods can also be useful in situations where there are. I couldn't think of a way to say that, so I'll let you have a stab at it. - Taxman ^Talk 14:58, 29 November 2005 (UTC)[reply]

How about getting really basic? Something about how we want analytic solutions. If we can't get them, then we go to approximate (with some control over error), and eventually to numerical (as a last resort). Additionally, aren't we really talking about solving potentially sophisticated problems using ONLY basic arithmetic (computing)? I'm just an undergrad, so I'm not qualified to contribute to the article yet, but this is how I see things. DB Nov 29 2005

That is a good point, and I was surprised to see that it is not mentioned in the article. It should definitely be mentioned somewhere. As you probably know, analytic formulas are not always preferable; sometimes, they are so complicated that it's hard to make sense of them. The relation between approximate / asymptotic and numerical results is even less straightforward. -- Jitse Niesen (talk) 13:35, 30 November 2005 (UTC)[reply]

So it could be said that we seek a practical analytic solution first. Failing that, we might pursue an approximate solution within a radius of convergence perhaps. Assuming this does not yield a practical solution, we attempt to find a numerical solution to describe our problem.

What about the point about numerical solutions are found using only basic arithmetic? Is that a valid point? DB, Nov 30 2005

I believed the "basic arithmetic" part needed to be removed. Left as it was, it sounded as if numerical analysts are merely adding and subtracting numbers--don't get confused here. . . this is not what we do in the profession. -- — Preceding unsigned comment added by 24.18.243.107 (talk • contribs) 07:55, 7 January 2006 (UTC)[reply]

I don't see your point. The basic steps in all algorithms are merely adding and subtracting numbers, and using these steps we solve complicated problems, don't we? I also don't like your edits which says that numerical analysis "is largely related to functional analysis". As I see it, the two main theoretical disciplines of maths used by numerical analysis are matrix theory and approximation theory, and matrix theory is usually not taken as a part of functional analysis. So I reverted your edit. -- Jitse Niesen (talk) 13:08, 7 January 2006 (UTC)[reply]

I have to agree with the anon at a certain point. There are better things to say in the introduction I think than that numerical analysis is done using addition and multiplication. While that's true, you could say in the same way that computer science is the study of things which are sequences of zeros and ones. So I would cut that part. Oleg Alexandrov (talk) 17:48, 7 January 2006 (UTC)[reply]

I see what you mean. It is indeed not that important by itself. However, the point is that we should distinguish in some way between numerical analysis and symbolic computation (see the above discussion). As far as I know, nobody has come up with a better way to achieve this then referring to these basic arithmetic operations. -- Jitse Niesen (talk) 21:58, 7 January 2006 (UTC)[reply]

I also believe "basic arithmetic. . . addition" is misleading and should be removed from the definition. This page should describe the core aspects of Numerical Analysis and it should be careful to distinguish itself from Numerical Methods. What is more, including "basic arithmetic. . .addition" is not only misleading, but it is incorrect. I am at a loss for words here . . . I think this should be clear to anyone who manages this entry; there are entire journals devoted to NA and these articles usually never even mention or include algorithms. One of the definitions I find useful is "Numerical Analysis is Functional Analysis with an emphasis on algorithms". — Preceding unsigned comment added by ExamplePuzzle (talk • contribs)

I don't like either the basic arithmetic or the functional analysis descriptions. But I don't have any suggestions. Oleg Alexandrov (talk) 09:33, 11 January 2006 (UTC)[reply]

Hey. I would not vote to use my "functional analysis with. . ." description on this page either. I was just trying to move the focus away from including "basic arithmetic". I will go ahead and remove it and then let other users read over it and offer their comments (this includes you :D).