Talk:Padé approximant

message: The epsilon algorithm, the page refers to for getting the coefficients is missing. A search leads to nothing. I'm not from that field and thus cannot contribute the missing page. 84.226.41.90 17:52, 21 January 2007 (UTC)
thread_title: where's epsilon?

message: (EDIT)
To study the resummation of divergent series, it can be useful to introduce the Padé o simply Rational zeta function as:
 \sum_{n=1}^{\infty} \frac{[N/M]_f(n)}{n^{s}}= \zeta _{Q}(s) 
so the zeta regularization value at s=0 it is equal to the 'sum' S, of the divergent series:
 S= \sum_{n=1}^{\infty}f(n)  
the functional equation for this Pade zeta as:
 \sum_{j=0}^{M}p_{j}\zeta _{Q}(s-j)= \sum_{j=0}^{N}q_{j}\zeta_{0}(s-j)  
here '0' means that the Pade is of order [0/0] and hence, we got the Riemann zeta function. and  Q=Q(n)=[N/M]_f(n)
Sorry.. for my edition, perhaps now it looks clearer from the coefficients of the upper and lower Polynomials involving Padè approximant  (If possible put it back) i thought i saw it into a book about Dirichlet series but can not remember its name.  
----
The above section appeared in the article. It looks to me as it is valid, but unfortunately I have no idea what's meant. In the first formula, the numerator seems to be independent of n; and what is Q? In the last formula, the a_j and b_j is not defined. -- Jitse Niesen (talk) 13:28, 23 October 2007 (UTC)
replies: text: Okay, it looks clearer now; thanks. I changed it a bit, hopefully without introducing any errors. -- Jitse Niesen (talk) 11:45, 26 October 2007 (UTC)
thread_title: Riemann-Padé Zeta function

message: Consider the introductory text:
Padé approximant is the "best" approximation of a function by a rational function of given order - under this technique, the approximant's power series agrees with the power series of the function it is approximating. The technique was developed by Henri Padé.
The external link "[1]" to "http://www.dattalo.com/technical/theory/sinewave.html" is inappropriate in a lead-in text. I have moved it into the references.
--Михал Орела 14:26, 11 November 2010 (UTC)
thread_title: Introductory text

message: In checking the Press et al. reference
* Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical recipes in C. Section 5.12., Cambridge University Press.
I noted that the given pdf link  no longer worked. In particular, I am
not sure that the book is "freely" available electronically according to the usual copyright meaning.
--Михал Орела 14:39, 12 November 2010 (UTC)
replies: text: I updated the Numerical Recipes reference to the current edition and fixed the link.
ServiceAT (talk) 01:03, 11 July 2011 (UTC)
thread_title: References

message: Found that the example for exp(x) was edited by some IP user in March, and becomes mathematically incorrect. 
https://en.wikipedia.org/w/index.php?title=Pad%C3%A9_approximant&type=revision&diff=769403635&oldid=769402974
However it could not be simply "undo" as there is conflicts. Can anyone help to revert the mal-edit?
Billyauhk (talk) 04:30, 18 November 2017 (UTC)
thread_title:  Can anyone help to revert an edit 

message: The example for exp(x) here: https://en.wikipedia.org/wiki/Padé_approximant#Examples does not match the example in the Padé table here: https://en.wikipedia.org/wiki/Padé_table#An_example_–_the_exponential_function.
I believe the Padé table is correct and this page is wrong. I haven't edited a page before and wanted to get confirmation from someone else that there is actually an error first.  — Preceding unsigned comment added by Aerojunkie (talk • contribs) 16:49, 15 March 2018 (UTC)
thread_title:  Is the exp(x) example wrong? 

message: function [A,B] = paday(c,p,q)
% c is the Taylor Approximation, col vector
% p the number of terms in the numerator A, and q the number of terms in the denominator B
Temp = sparse(p+q+1, q+1);
for iq = 1:q+1
    temp(iq:length(c), iq)=c(1:length(c)-iq+1);
end
B = -Temp(p+2:p+q+1,2:q+1)\c(p+2:p+q+1);
A = Temp(1:p+1,iq+1)*(1;B)
QuentinUK (talk) 13:50, 9 December 2018 (UTC)
thread_title:  Simple example MatLab code 

message: I just coded up that approximation.  Return values are worse than single precision floating point for abs(x) > one sigma = sqrt(2)/2 and are completely unacceptable for abs(x) > two sigma.
In addition to some citations, these examples need error bounds or they should be removed.  It is really morally wrong to waste people's time with bad algorithms.  — Preceding unsigned comment added by 154.20.183.43 (talk) 22:08, 13 February 2019 (UTC)
thread_title:  Pade approximation of erf(x) example is really '''bad''' 

message: Many examples have highest order terms (say) first in the numerator, but bottom in the denominator. There is no consistency.
63.145.59.55 (talk) 17:17, 7 December 2020 (UTC)
thread_title:  Examples switch polynomial conventions 

message: It says that the Padé approximant [p/q]_f is unique, but from the definition it seems that for f(x)=0 both \frac{0}{1+x} and \frac{0}{1+2x} would go as [1/1]_f. How to properly define uniqueness then? adamant.pwn — contrib/talk 11:44, 6 April 2022 (UTC)
replies: text: On the other hand, I don't see any way for e. g. [1/3]_f to exist for f(x)=x^2. The way it's defined in the article, [1/3]_f will start from either a_0 or a_1 x, which can't match x^2 in first 4 terms. adamant.pwn — contrib/talk 19:07, 6 April 2022 (UTC)
replies: text: I came across the same problem. The point is that the Padé approximation does not always exist! This should be mentioned more explicitly in the article. Benji104 (talk) 17:11, 31 August 2023 (UTC)
thread_title:  Uniqueness