User talk:Jitse Niesen

Nice job on the numerical ordinary differential equations page.

Thanks. Rednblu 19:09 19 Jul 2003 (UTC)

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Hi there, and welcome to the 'pedia! Impressive work so far -- just one request: could you try to avoid hard line breaks within paragraphs? This makes text harder to edit, and breaks list formatting. --Eloquence 21:02 19 Jul 2003 (UTC)

Okay, I will try to remember that. Thanks for repairing it. Jitse Niesen 11:02 20 Jul 2003 (UTC)

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Hmm, the ugly LaTeX thing is definitely unfortunate. I think using LaTeX in running text is the right thing to do though, and hopefully the ugliness will be fixed at some point. The math source is often nearly unreadable when marked up with <sup> tags and whatnot, not to mention that it ends up typesetting the variables in a standard italicized font rather than the math font, which looks odd. It also makes rendering to non-HTML formats, like a future print version, more ugly, since again the variables won't be properly rendered in the math font. --Delirium 23:33, Jun 23, 2004 (UTC)

Just to clarify, I'm not reverting back to it. By saying it's the right thing to do, I meant in theory, and hopefully also eventually in practice, when the layout problem gets fixed. --Delirium 00:24, Jun 24, 2004 (UTC)

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Thanks for fixing Lebesgue integration. I did not notice I was edited and older version. MathMartin 00:06, 4 Sep 2004 (UTC)

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I'm sure that what you discussed on my talk page should be appropriate :) Dysprosia 00:20, 10 Sep 2004 (UTC)

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I replied to you kind comment re Simon Donaldson on my talk page (so I'm writing this in case you didn't set a watch on my talk; it Feel free to delete this comment when read!). I note your discusion above re in-line LaTeX. Billlion 21:29, 14 Sep 2004 (UTC)

numerical analysis

Hi, we have met on a few numerical analysis pages. If you have any spare time it would nice if you could check Chebyshev polynomials and especially Chebyshev polynomials#Polynomial interpolation for errors.MathMartin 20:55, 15 Sep 2004 (UTC)

I rewrote Chebyshev nodes but I am not really satisfied. Feel free to improve my notation. More generally I intend to rewrite most of the spline pages which are in a really bad shape and contribute to many article on numerical analysis in the next few weeks. As the material is new to me I will probably make some mistakes and often lack the necessary broader scope. It would be nice if you could keep a watchful eye on me.MathMartin 11:07, 19 Sep 2004 (UTC)

You seem to be writing faster than I can check! This is of course good as many numerical analysis pages are indeed far worse than I'd like. In my opinion, the main problem with Wikipedia is not that we don't have enough articles, but that they are not good enough, but that's another issue. I don't know that much about splines, but I'll do my best.

Yes did quite some editing today :).

Where did you get the ||·||₀ notation for maximum norms from? I'd use ||·||_∞ (see e.g. Lp space), but perhaps I'm too theoretically minded. Similarly, for me the space C₀[−1, 1] is the space of continuous functions f with f(−1) = f(1) = 0.

I have seen ||·||₀ in a book but now I believe it is a printing error as I could not find any use of this notation on the web. I will change it to ||·||_∞. As for C₀[−1, 1], I meant to write C⁰[−1, 1].

Hopefully, I'll soon find time to write a bit about the Lebesgue constant, which seems to be the thing you were leading up to. O yes, one last note: I personally think that references should be provided with every article, to help the reader and also out of honesty. You don't need to give a references for every statement (though I wouldn't mind if you did!).

I agree there should be more references. But unfortunetely at the moment I get my knowledge from the numerical math script I am studying so I am unable to provide references.

Your edits to Chebyshev nodes made the article much clearer. Dank je wel.MathMartin 22:20, 19 Sep 2004 (UTC)

Runge phemonena

Hi, I have a question concerning Runge's phemonena. When using Chebyshev nodes to interpolate a function we can minimize the interpolation error, but the interpolation error still increases when we increase the degree of the polynomial. Is this true ?MathMartin 19:58, 20 Sep 2004 (UTC)

Different matrix notation

Do you know of any difference between the matrix notation

${\begin{bmatrix}1&0\\0&5\end{bmatrix}}$

and

${\begin{pmatrix}1&0\\0&5\end{pmatrix}}$

Which one is more common ? MathMartin 17:28, 25 Sep 2004 (UTC)

Rate of convergence

Thanks for editing this page. I only created it as a quick hack because an anon added this text at a really inopportune place. I probably should have listed it on cleanup... anyway it looks nice now. Gadykozma 00:36, 20 Oct 2004 (UTC)

Federigo Enriques

Oops. I had a bunch of windows open and must've pulled that by accident. It'll go back in a second. --DMG413 01:46, 20 Oct 2004 (UTC)

For the chage of bilinear interpolation.

Yup, sorry, I was confused by the diagram. The Interpolation formulas are right.

Regards,

GunRock 16:22, 25 Oct 2004 (UTC)

Changes in the statement of Weierstrass's theorem

I replaced real with complex because that gives, according to Walter Rudin's book Principles of Mathematical Analysis, the theorem as "originally discovered by Weierstrass". There are two reasons why I rely on that. The first one is that a large part of Rudin's mathematical research was about generalizing the (Stone-)Weierstass theorem, and the second one is that his book (the one mentioned above) is known to have hardly any errors (if at all; I've never heard of one) and typos. A polynomial over C has its coefficients in C.

The Bilinear Interpolation

Yes, now the graph is much better, but usually, I think a point with a name Q_m, should have a coordinate (x_m,y_m), that may make a better sense. Thanks very much for your earnest. :GunRock 03:24, 27 Oct 2004 (UTC)

The Bilinear Interpolation

Hi there, thanks, and the diagram of the interpolation should be changed either. Thanks! GunRock 06:30, Oct 28, 2004 (UTC)

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Nifty. :) Dysprosia 12:37, 5 Nov 2004 (UTC)

Newton's method

I thought about it for a long while, and I think you are right, 'to find' is better than 'to finding'. --Oleg