Talk:Householder's method

message: The first equation under motivation has a problem.  First term should be 1/(f(x)-f(a)), not 1/f(x).  There is also a problem with the first sentence of the first paragraph.  Has a second what?
::Yeah, but since f(a)=0, that is really the same expression. I added some words in that respect. Sorry for the second ..., this was a copy-paste from Halley's method.--LutzL (talk) 12:19, 30 December 2007 (UTC)
thread_title: First equation has problems

message: Some editor was bold and asked
What is a 'simple zero'? What is a simple pole? Why 1/(x-a) and not 1/(f(x) - f(a))?
directly in the article. 1) Simple zero was directly explained as a root where the derivative is nonzero. In other words, a root of multiplicity one. 2) A simple pole is in the same manner a pole singularity of multiplicity one. The last question should be elaborated, since f(a)=0 and the approximate behaviour of 1/f(x) was to be discussed.--LutzL (talk) 17:29, 22 February 2010 (UTC)
thread_title:  Questions in ''Motivation'' 

message: 10-gauge00 Some guy who have contributed nothing to this page said that " previous derivation is more concise and clearer, and we don't need another one ", I think it is personal or individual preference to determine which one is more concise and clearer, and if someone who can not understand another derivation, think that is nore complicated and unclearer, and have difficult to understand that derivation, he should spend more time to study mathermatics instead of deleting that derivation of this page. Once again, your difficulty of understanging the another derivation is not my fault and wikipedia's fault. Before deleting the derivation, you should think about your personal ability of maths. Furthermore if somone is eager to say to a derivation sould be deleted in the case that there exists a more compact, easy to understand, more elegant, then it is the same to say that all the article should NOT contain another derviation. If I expended further this thought, if someone said that if a derivation should be deleted by the very reason that there exists more compact, clearer one, I'd like to say, go out to the street, and find someone who is more handsome, earns more money, married more beautiful girl, after finding him, then shoot yourself, by the very reason that there exists more clearer and more concise person. (Gauge00 (talk) 09:52, 17 May 2010 (UTC)
replies: text: 11-Gandalf61 That "some guy" is me. I deleted your "new derivation" because it simply repeats the special cases from the "Methods of lower order" section, with some tedious algebraic derivations. It offers no insights into why Householders method works in general. And it contains several erros - the correct terms are Taylor expansion, Newton's method and Halley's method, for example. I did not say I could not understand it - I can follow it, but it adds nothing useful to the article. As for the rest of your rant, you need to realise that this type of belligerent and obnoxious abuse is not going to win you either friendship or respect in the Wikipedia community. Gandalf61 (talk) 10:17, 17 May 2010 (UTC)
replies: text:  12-gauge00 It is ridiculous that Taylor expansion, Newton's method and Halley's method are erros. I know I used type Tailor something in the page, I did not corrected it, I know, but I was too busy to check spelling check, grammer check, etc. And If you have noticed them, you should corrected them until I did it instead complaining about them. And please dont say Newton method is not correct but Newton's method is. At least wikipedia did not make Newton method link to red link, the broken link, like Newtooown method . And I am glad to hear you could understand my new derivation. But how on earth didn't you realize than my derviatin contains the method how to calculate the  (d^{n}/d^{n}x) (1/(f(x))  Do you know that calculation of  d^4/d4(x)(1/f)  is so terrible? I will include it in the future beliveing  d^4/d4(x)(1/f)  would be useful to someone even if you dont need it. And you should realize that my derivation contains a relation between Halley method and Newton method, and also contains between d'th order method and d+1'th method.  And you said it adds nothing useful to the article. You should realize that the determination my addition would be usefull or not is NOT the duty or priviledge of you. You are not the sole, unique reader, unique referee. Gauge00 (talk) 11:00, 17 May 2010 (UTC)
replies: text:  13-LutzL Your addition is badly readable. The principal ideas of the calculations are barely exposed. And where something is exposed, it is largely exaggerated. For instance, I cannot see a derivation of the method. Because that derivation would have to explain the convergence orders. What is contained is a badly explained procedure for computing the derivatives of 1/f from those of f. But the notation is unusual and very hard to read. There may be some insight in your additions, but it is hard to detect in your formula desert.--LutzL (talk) 11:45, 17 May 2010 (UTC)
replies: text:  14-gauge00 If I understanded correctly your saying as that my article has no derivation part of the method, could I said that my derivation was one of the mathematical induction? Case 1 is true; using case 1, case 2 is true; using case 1, case 2, case 3 true. is the type of the mathematical induction (Gauge00 (talk) 20:54, 17 May 2010 (UTC)

text:  15-Gandalf61  I have placed a note at Wikipedia talk:WikiProject Mathematics asking other interested editors to add their views to this discussion. Gandalf61 (talk) 12:01, 17 May 2010 (UTC)

text:  16-gauge00 Questions; please specify the place where I exaggerated; where is the badly explaned part in the procedure for computing the d of 1/f. What notation is the notation you said that it is the unusual very hard to read; and i'd like to know whether of not you still do not know the reason why I did the derivatives of 1/f at first to get :-fD^{(n)} = C(n, 1)D^{(n-1)}f^{\prime} + C(n, 2) D^{(n-2)} f^{\prime\prime} + C(n, 3) D^{(n-3)} f^{\prime\prime\prime} + ... + C(n, n) Df^{(n)} ? (Gauge00 (talk) 12:12, 17 May 2010 (UTC)

text: 17-Paul Carpenter There's no doubt the presentation of the alternative derivation is very poorly presented. It could be made neater, more concise and significantly clearer. None of that dictates that it shouldn't be there. Pending the dramatic improvement of that section (and probable demotion to subsection of ==Derivation==) I don't see why it should be completely removed. However, repeating the contents of the methods of lower order is entirely unnecessary and does indeed add nothing to article. Paul Carpenter (talk) 13:33, 17 May 2010 (UTC)
thread_title:  08:00, 17 May 2010 --- First deletion by [[User:Gandalf61|Gandalf61]] 

message: (30-gauge00) --- R.e.b deleted my article. You did not write any thing on talk page. You should know that there are lots of people who can delete my article, but the right should be gone to the people of talk page, including me. I think the people who complained about my page have privilege of deleting the article. (Gauge00 (talk) 19:26, 17 May 2010 (UTC)
replies: text: (33-gauge00) ---  User:Paul_Carpenter said that None of that dictates that it shouldn't be there, and I don't see why it should be completely removed. You are saying that the Paul is not faver of keeping the new material. Answer me.(Gauge00 (talk) 20:54, 17 May 2010 (UTC)

text: (34-gauge00) ---  For me, RDBury is a liar; I thought Paul Carpenter perfers keeping, but RDBury neglected him. (Gauge00 (talk) 21:07, 17 May 2010 (UTC)
thread_title:   16:18, 17 May 2010 --- 3rd deletion by R.e.b 

message: ::(40-Savonneux) --- Im not even sure where to reply in this mess but is it necessary to have an impenetrable (i.e. tedious) derivation tacked on? The one already there illustrates the concept. This doesn't add anything except a lot of scrolling. --Savonneux (talk) 02:46, 18 May 2010 (UTC)
replies: text:  (41-gauge00) --- Specify the one that you said The one already there. Please before deletion, think about that if it looks like just a scrolling, it not the fault of the derivation, but could be the fault of yours. And this talk is on going, the talk users could know more about the this talk history, please give them the priviledge of the deletion. I'd dont like a guest who came my house, lying in my bedroom. It seem you came right before, and arrogantly deleted my drivation, didn't you. (Gauge00 (talk) 02:58, 18 May 2010 (UTC)
replies: text:  (42-gauge00) --- You said that The Methods of computing square roots has a bunch of algorithms that are historically significant without their own pages. This page is just Newton's method and Shifting nth root algorithm for finding \sqrt[3]{x} both of which apply to nth roots not just cubics. gauge00 started to say.... in the articleMethods of computing cubic roots, my algorithm contains  (k + a_1 10^{-1} + a_2 10^{-2} + a_3 10^{-3} + ...)^3  expansion series, in the article, the deleted article; Then do you think the expansion could be used to get the 4th root, and 5th root, 6th root also??? Why you can't see the superscipt 3 on the  (k + something + ...)^3  Dont make statement when do not know something. (Gauge00 (talk) 03:16, 18 May 2010 (UTC)
replies: text: (43-Savonneux) ---  The contents of that AFD changed considerably from nomination till the end, and yes it had examples of methods that already had articles. It's also a completely different issue that is closed. Meh. --Savonneux (talk) 04:05, 18 May 2010 (UTC)
replies: text: (44-gauge00) ---  The expansion series was the esseential part to compute cubic root, and it was there from the beginning. the expansion could be used to solve cubic root, only cubic root.  So You did false statement, it means, you did not understand my method, as most othes did not. From this basis, I do uncertain your math. (Gauge00 (talk) 04:24, 18 May 2010 (UTC)
replies: text:  (45-gauge00) ---  Hey, Savnneux, your name sounds like a French, I know a few french words, gateux, chateau, eau, plateaux, surely I sould not drop the manteaux, any way what I want to say is that I added some material in Methods of computing square roots, in a section of 'Babylonian method and arithmetic mean'. I'd like to show how arithmetic mean is related to the Babylonian method. The reason I said this here is that you and RDBury, the reference checking machine, would be very happy to hear that I added something material without any references. Surely you two would visited that page, and contribute that page by deleting. (Gauge00 (talk) 05:11, 18 May 2010 (UTC)

text:  (46-gauge00) --- User:Gandalf61 was the supportor of the deletion of the Methods of computing cubic roots, maybe came along with me, like a stoker, haha. RDBury, savoneux, Gandalf61, three came along here following me. These three guys came here, and deleted my derivation; at first, by Gandalf, at 2nd by RGBury, 4th by savoneux.  The cooperations of you three guys works very well.  And Gandalf said that individual methods already have their own articles, please if you dont understand, dont say anything. Where did you find my digit by digit method in the wiki?? Where? If you can, give the link to me. By giving that link, you can stop me.  (Gauge00 (talk) 05:46, 18 May 2010 (UTC)
thread_title:   02:49, 18 May 2010 --- 4th deletion by [[User:Savonneux|Savonneux]] 

message: Gandalf61, who deleted at the first, and had placed a note at Wikipedia talk:WikiProject Mathematics, deleted once again, leaving message rv - consensus is that new section should be removed - please accept this and stop edit warring. (Gauge00 (talk) 09:20, 18 May 2010 (UTC)
replies: text: (61-gauge00) --- Gandalf61 said in (25-Gandalf61) that Four different editors have responded to you in this thread. All four of us agree that your new section does not improve the article. That is called consensus gauge00 once agin asks you to specify the four different editors. You Gandalf61, 1st deletor, and RDBury, 2nd deletor, LitzL if you want (13-LutzL), and who?? (Gauge00 (talk) 10:54, 18 May 2010 (UTC)
replies: text: Paul Carpenter had also said above: "repeating the contents of the methods of lower order is entirely unnecessary and does indeed add nothing to article". You are beginning to sound petty and obsessive. I suggest you take a Wikibreak and calm down a bit. Gandalf61 (talk) 12:06, 18 May 2010 (UTC)
thread_title:  07:45, 18 May 2010 --- 5th deletion by [[User:Gandalf61|Gandalf61]] 

message: 104th I never know about blocking system of wiki, even though somehow where exists some mechanism to settle stallmate. Anyway as I wrote in this talk page, I did 4th reverted, including not-login state reverting, and I was warned of blocking from someone, even though I do not know the blocking period. Anyway I prepared blocking state by copying my derivation to my name space, to those who want to know about my derivation. My derivation of Householder's method can be found at User:gauge00/Householder. (Gauge00 (talk) 04:56, 18 May 2010 (UTC)
thread_title:  preparation for blocking 

message: I performed the usual searches for references on this subject but am having trouble finding anything usable. MathWorld covers something it calls Householder's method, but it's really a variation on Halley's method and doesn't support the material given here. A Google search turned up dozens of sources for "Householder's method" but every one of them seems to be referring to the Householder transformation which is a completely different subject. That leaves the site given in the External links section and the 1970 book by Householder that it cites. (For some reason I can only view the site in IE and Firefox just displays question marks; I'd appreciate it if someone else could try the link in Firefox and let me know what they see.) The site is self published and so does not meet WP's criteria for reliable sources, but even you accept it as a source it seems to use the phrase "Householder's method" in the sense of "a method invented by Householder" not in the sense of "the algorithm commonly known as 'Householder's method'". So it appears that the phrase "Householder's method" with this meaning is in fact a neologism and a different name should be found for the article. In any case, some work is seriously needed to establish both the notability of the subject and reliable sources for the content.--RDBury (talk) 17:11, 17 May 2010 (UTC)
replies: text: By what reason did not you answer my questions? And to me it is too funy that such a simple Householders method should have some references.  Giving and receiving a reference makes a money for example, err, 10 dollars? Selling references could be huge business. Why did not think about something like 'derivaiton' and 'formal derivation', or 'rigorous derivation', etc??? should I have attach references to the fact that  d(ln(x)/dx = 1/x  like? (Gauge00 (talk) 19:45, 17 May 2010 (UTC)

text: Coulumbus discovered America. Then Coulumbus should attached some proofs that he discovered america? If Coulombus could not give his proof, you should travel to America and makes proof instead of Columbus, instead of complaining 'Coulumbus is liar, should be jailed, executed'. Is it the common phenomenon that a geneous, like Einsten, made a big leap, then lots of common people are eager to fill the gaps that the genious made. (Gauge00 (talk) 19:54, 17 May 2010 (UTC)
thread_title:  References 

message: Notation can be pretty opaque sometimes if you don't already understand the idea. Pictures can often be groked in a single glance.  Just a suggestion.  —Preceding unsigned comment added by 98.210.32.163 (talk) 07:13, 26 May 2010 (UTC)
thread_title:  This article needs pictures 

message: I believe this method is due to Schröder.  The name "Householder's method" appears to be due to the article "Newton’s method and high order iterations" by Sebah and Gourdon , but Householder did not claim to invent the method.  Householder credits Schröder for the method.  The Wolfram MathWorld article on Schröder's method  cites appropriate references, including the book by Householder that describes this particular instance of Schröder's method (Theorem 4.4.2).  — Preceding unsigned comment added by 129.55.200.20 (talk) 19:55, 20 March 2012 (UTC)
thread_title:  Title should be Schröder's method 

message: Substituted at 02:13, 5 May 2016 (UTC)
thread_title: Assessment comment

message: What this article badly needs, but does not have, is a proof of the statement
:| x_{n+1} - a | \le K \cdot {| x_n - a |}^{d+1} , for some K > 0.\!
And in particular a way to determine the value of K so that I can tell just how useful these methods actually are. JRSpriggs (talk) 05:14, 1 May 2018 (UTC)
thread_title:  Higher order convergence? 

message: Wouldn't it be better to write the equation under "Method" as
:x_{n+1} = x_n + d\; \frac {\left(f\right)^{d}(x_n)} {\left(f\right)^{d-1}(x_n)} 
rather than taking recropicals of the function in the numerator and denominator?
Bubba73 You talkin' to me? 01:12, 11 May 2024 (UTC)
replies: text: The derivative of a reciprocal is not the same as the reciprocal of the derivative.  —Quantling (talk | contribs) 23:43, 11 May 2024 (UTC)
replies: text:  The notation was not clear to me.  So you take the derivatives of the reciprocal of the function, right? Bubba73 You talkin' to me? 02:21, 12 May 2024 (UTC)
replies: text: Yes.  The superscript  and superscript  indicate the number of times to differentiate.  —Quantling (talk | contribs) —Quantling (talk | contribs) 15:32, 13 May 2024 (UTC)
thread_title:  How to write the equation