Talk:Ritz method

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Does anyone know if the Ritz method was actually pioneered by Walter Ritz, or was it simply named in honor of him? He died in 1909, so I am wondering how he could have developed such a method (from my understanding, the use of such methodology would require the Schrodinger equation and other techniques that were still 20 years off...) Any mathematical or physics historians have information on this? Nimur 18:29, 15 May 2006 (UTC)

This is the same principle as Rayleigh-Ritz method

Please, read:

E. Butkov, Mathematical Physics, "Variational Methods", section 13.5
G. Arfken, Mathematical Methods for Physicists, "Calculus of Variations", section 17.8

You must understand that Wave Mechanics (Quantum Mechanics), Electromagnetic Waves, and Acustic Waves are the same mathematical formalism, satisfying the Sturm-Liouville problem, and belonging to Hilbert Space solutions.

Rayleigh-Ritz method is exactly the same as Ritz method. The preceding unsigned comments were left by User:143.107.133.29

Please sign your edits using four tildes, ~~~~; and consider creating an account to help track your edits. I will look into this issue further; at first glance, I did not agree with the merge, but I will re-read some of my texts as well as your suggested papers. Perhaps a merge should be part of a larger rewrite to establish context for the technique. Check back here at the talk page for further updates. Nimur 19:27, 30 August 2006 (UTC)

I created a acount. Thank you for your advise! RafaelBarreto 20:04, 30 August 2006 (UTC)

I oppose the merge. It seems to me that the merged article would have to have two sections, one for physicists, one for engineers, so we might as well have two articles. I hav been asked to expand the RR page as well, if it comes down to it. Greglocock 02:11, 29 September 2006 (UTC)

For a more abstract formulation of Ritz method

IMO right now this article is unnecessarily complicated with quantum mechanics. It would be much better to use a more abstract (and thus easier to understand) formulation. Some information on minimizing sequences or an appropriate link would be nice, too. 95.181.12.52 (talk) 15:19, 29 December 2009 (UTC)

• Indeed. It is clear by this article that he original author is too attached to quantum mechanics to be able to understand the simplicity of this method without turning to needlessly complicated and secondary concepts. -- Mecanismo | Talk 20:49, 23 July 2010 (UTC)

How is the equation solved efficiently?

The article derives the equation

$\det \left(H-\varepsilon S\right)=0,$

which apparently should be solved in order to find the eigenenergies of the system. If a well-modelled system is desired, I guess that many basis functions have to be used, and for large matrices (which result from a large number of basis functions), just calculating the determinant can be an intricate task, requiring LU decomposition in order to be efficient (which is by the way only possible when the matrix is known, which is not the case in this equation since $\varepsilon$ is unknown).

So how can this equation be solved efficiently? I guess expanding the determinant is out of question, since it is likely to yield a very complex polynomial. —Kri (talk) 02:59, 4 January 2016 (UTC)

Merge proposal

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

Unanimous consent. MinervaKizyna (talk) 13:13, 14 June 2024 (UTC)

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As discussed by RafaelBaretto (talk · contribs) in the earlier discussion "This is the same principle as Rayleigh-Ritz method", this is the same principle as Rayleigh-Ritz method, and so I propose that Ritz method is merged with that: see the two sources in that discussion, as well as Suli and Mayers, An Introduction to Numerical Analysis, section 14.2.

User Greglocock (talk · contribs) opposed the merge in 2006 as 'the merged article would have to have two sections, one for physicists, one for engineers' but since then the section for engineers has been moved to this page. In fact, as mentioned in the discussion "For a more abstract formulation of Ritz method", this page discusses the same method twice, once using quantum physics language and then a second time using engineering language. The Rayleigh-Ritz method page discusses the exact same concept a third time but using some simplifications that you get from the system being finite-dimensional. What I think is needed is one page which gives the general mathematical description for an operator on a Hilbert space (I'd be happy to write this), and then the applications in matrices, physics, engineering... as example sections.

In fact, the Rayleigh-Ritz method page says "mathematically the same algorithm is commonly called the Ritz-Galerkin method", which then links to the Galerkin method page, and the link 'Ritz-Galerkin method' on the Galerkin method page links to this page. Furthermore, the section on attribution and naming in the Rayleigh-Ritz method page discusses that the same algorithm is called the Ritz, Rayleigh-Ritz, and Ritz-Galerkin method by different authors, so I think all three names should direct to the same page. MinervaKizyna (talk) 13:20, 3 June 2024 (UTC)

Support See also Rayleigh–Ritz_method#Naming_and_attribution Johnjbarton (talk) 14:08, 4 June 2024 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.