![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||||||||||
|
I removed the paragraph on Chomsky as I felt it inappropriate in an article whose main topic is the mathematical sense of 'order of approximation'. Zero sharp 05:03, 19 November 2006 (UTC)
While orders of approximation are used for data fitting, they are also used in theory work. The zeroeth order, first order, second order expansions are used when the relevant terms in the expansion series become significant enough to affect theoretical predictions. This should be made more clear. "First order" and "Second order" effects are often used to describe perturbations and deviations from linear models. We should have some text on this. -- ScienceApologist 14:03, 2 December 2006 (UTC)
I'm having a hard time understanding the purpose of this article. It has already been flagged for having no sources, the information in the article seems largely subjective, and if other people are like me then the information that they are actually looking for is in the Taylor Series article. 67.128.198.190 ( talk) 20:32, 8 March 2013 (UTC)
This article is necessary because it explains something else than the Taylor Series article. The Taylor Series article does not make any references to orders of precision/approximation that are useable by the general audience.
--
Jangirke (
talk) 20:50, 21 March 2013 (UTC)
The current article strikes me as trying to merge two separate issues into one: 1. the number of significant digits in the estimation of a quantity. 2. the degree of a polynomial fit. I suggest it would be far more pedagogical to treat these two issues separately. / 216Kleopatra ( talk) 21:15, 17 October 2013 (UTC)
The discussion started here on the need for a new section with examples of "historic approximations", where order of approximation was very important for some reasons. Suggestions are invited, in addition to the three topics already mentioned. The descriptions should not be too long, as this section is should not substitute for full articles. — Preceding unsigned comment added by C. Trifle ( talk • contribs) 15:43, 26 March 2016 (UTC)
User:Pacerier added "Unclear" tables to three units. User:Pacerier was very active on April Fools Day and on a day before making lots of contributions to different articles. In fact, the remark that the text may be unclear to readers could be added to just any text but I do not think the added criticism was just a practical joke. In my opinion, a graph to show the three examples would help. Also, this article should be extended by more examples (see above). C. Trifle ( talk) 19:45, 2 April 2016 (UTC)
Order of approximation may refer to
Most posts in this talk page complain that the this article is unclear and confusing. It appears that one reason is that it mixes two different notions of order of approximation. It has been recently suggested to transform this article into a disambiguation page, whose content is given in the preceding section. As this article belongs to four different projects, the discussion between only two editors is no sufficient for such a dramatic change. D.Lazard ( talk) 14:29, 4 April 2016 (UTC)
What to do with the information for general reader? I have read some old edits since 2003. I think the intention was good but there was some danger of confusion from the beginning. One might understand that if you have some three points then you begin with zero significant digits and as a result you get a constant, after which you get one significant digit and a slope, and then two digits for a parabola with which most scientists are happy and here they usually end. IMO the problem is that there is defintely a need in Wikipedia for something that is not given in this article, but should be placed somewhere. I mean a bit more reliable piece for the general reader. (1) the phrase "order of approximation" is generally used in language in various contexts (2) there was some historic usage that does not match today's views. C. Trifle ( talk) 09:04, 8 April 2016 (UTC)
The "main/reference article" about the subject, Scale analysis (mathematics), is "didactically horrible"... A merge will not solve the problem.
Articles to use as "reference article" are Big O notation and Curve fitting: the order of approximation is a jargon about "scientific modeling of reality". See curve fitting: can use similar illustrations, and here (the order of approximation article) can also add more generic illustrations, not only linear curves, but any other "fit to model" process (as "progressively more refined approximations" process)... see Scientific modelling.
-- Krauss ( talk) 08:55, 12 April 2016 (UTC)
The lack of clarity in the examples could be reduced by drawing a simple graph for each example.• • • Peter (Southwood) (talk): 05:50, 19 April 2016 (UTC)
I have changed the introduction a bit and added the references section and links to dictionaries and inside Wikipedia. There seemed to be some confusion about the usage of phrases with and without "order", and also the meaning of "precision" and "accuracy". It is waiting in my Sandbox. Is it better or worse? How to improve it? C. Trifle ( talk) 14:04, 2 June 2016 (UTC)
...is an approximate fit to the data, obtained by simply averaging the x-values and the y-values. (Stop here.) After that, it is necessary to show when we need to ...derive a multiplicative function for that average... here or in the next section because that seems to fit better to introducing the first order approximation. -- C. Trifle ( talk) 00:53, 26 November 2019 (UTC)
I looked at the following articles: Order of approximation, Taylor's theorem, Taylor series, and Big O notation. They all user the word "order" without defining it. Links to this page would help. I propose to begin this discussion with the use of a Taylor series to approximate a simple function. I would like to place this soon after the following sentence:
"The formal usage of order of approximation corresponds to the omission of some terms of the series used in the expansion (usually the higher terms)."
I will remove the comment "(usually the higher order terms)" and instead give an example where the higher order terms are omitted. Then I will Taylor expand the inverse of (1+x) (exponential function), and identify the terms.
Guy vandegrift (
talk) 04:11, 10 June 2024 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||||||||||
|
I removed the paragraph on Chomsky as I felt it inappropriate in an article whose main topic is the mathematical sense of 'order of approximation'. Zero sharp 05:03, 19 November 2006 (UTC)
While orders of approximation are used for data fitting, they are also used in theory work. The zeroeth order, first order, second order expansions are used when the relevant terms in the expansion series become significant enough to affect theoretical predictions. This should be made more clear. "First order" and "Second order" effects are often used to describe perturbations and deviations from linear models. We should have some text on this. -- ScienceApologist 14:03, 2 December 2006 (UTC)
I'm having a hard time understanding the purpose of this article. It has already been flagged for having no sources, the information in the article seems largely subjective, and if other people are like me then the information that they are actually looking for is in the Taylor Series article. 67.128.198.190 ( talk) 20:32, 8 March 2013 (UTC)
This article is necessary because it explains something else than the Taylor Series article. The Taylor Series article does not make any references to orders of precision/approximation that are useable by the general audience.
--
Jangirke (
talk) 20:50, 21 March 2013 (UTC)
The current article strikes me as trying to merge two separate issues into one: 1. the number of significant digits in the estimation of a quantity. 2. the degree of a polynomial fit. I suggest it would be far more pedagogical to treat these two issues separately. / 216Kleopatra ( talk) 21:15, 17 October 2013 (UTC)
The discussion started here on the need for a new section with examples of "historic approximations", where order of approximation was very important for some reasons. Suggestions are invited, in addition to the three topics already mentioned. The descriptions should not be too long, as this section is should not substitute for full articles. — Preceding unsigned comment added by C. Trifle ( talk • contribs) 15:43, 26 March 2016 (UTC)
User:Pacerier added "Unclear" tables to three units. User:Pacerier was very active on April Fools Day and on a day before making lots of contributions to different articles. In fact, the remark that the text may be unclear to readers could be added to just any text but I do not think the added criticism was just a practical joke. In my opinion, a graph to show the three examples would help. Also, this article should be extended by more examples (see above). C. Trifle ( talk) 19:45, 2 April 2016 (UTC)
Order of approximation may refer to
Most posts in this talk page complain that the this article is unclear and confusing. It appears that one reason is that it mixes two different notions of order of approximation. It has been recently suggested to transform this article into a disambiguation page, whose content is given in the preceding section. As this article belongs to four different projects, the discussion between only two editors is no sufficient for such a dramatic change. D.Lazard ( talk) 14:29, 4 April 2016 (UTC)
What to do with the information for general reader? I have read some old edits since 2003. I think the intention was good but there was some danger of confusion from the beginning. One might understand that if you have some three points then you begin with zero significant digits and as a result you get a constant, after which you get one significant digit and a slope, and then two digits for a parabola with which most scientists are happy and here they usually end. IMO the problem is that there is defintely a need in Wikipedia for something that is not given in this article, but should be placed somewhere. I mean a bit more reliable piece for the general reader. (1) the phrase "order of approximation" is generally used in language in various contexts (2) there was some historic usage that does not match today's views. C. Trifle ( talk) 09:04, 8 April 2016 (UTC)
The "main/reference article" about the subject, Scale analysis (mathematics), is "didactically horrible"... A merge will not solve the problem.
Articles to use as "reference article" are Big O notation and Curve fitting: the order of approximation is a jargon about "scientific modeling of reality". See curve fitting: can use similar illustrations, and here (the order of approximation article) can also add more generic illustrations, not only linear curves, but any other "fit to model" process (as "progressively more refined approximations" process)... see Scientific modelling.
-- Krauss ( talk) 08:55, 12 April 2016 (UTC)
The lack of clarity in the examples could be reduced by drawing a simple graph for each example.• • • Peter (Southwood) (talk): 05:50, 19 April 2016 (UTC)
I have changed the introduction a bit and added the references section and links to dictionaries and inside Wikipedia. There seemed to be some confusion about the usage of phrases with and without "order", and also the meaning of "precision" and "accuracy". It is waiting in my Sandbox. Is it better or worse? How to improve it? C. Trifle ( talk) 14:04, 2 June 2016 (UTC)
...is an approximate fit to the data, obtained by simply averaging the x-values and the y-values. (Stop here.) After that, it is necessary to show when we need to ...derive a multiplicative function for that average... here or in the next section because that seems to fit better to introducing the first order approximation. -- C. Trifle ( talk) 00:53, 26 November 2019 (UTC)
I looked at the following articles: Order of approximation, Taylor's theorem, Taylor series, and Big O notation. They all user the word "order" without defining it. Links to this page would help. I propose to begin this discussion with the use of a Taylor series to approximate a simple function. I would like to place this soon after the following sentence:
"The formal usage of order of approximation corresponds to the omission of some terms of the series used in the expansion (usually the higher terms)."
I will remove the comment "(usually the higher order terms)" and instead give an example where the higher order terms are omitted. Then I will Taylor expand the inverse of (1+x) (exponential function), and identify the terms.
Guy vandegrift (
talk) 04:11, 10 June 2024 (UTC)