# What is the right citation for the power iteration method to find eigenvalues?

What is the right citation for the power iteration method to find eigenvalues, if I want to cite the method in a paper? I've seen some Google PageRank references in this context. But Brin and Page didn't invent the power iteration method, did they?

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Nobody expects you to be a historian. If the provenance isn't clear, why not just cite who you think is responsible, and include citations from other papers who mention the topic? Nobody is going to accuse you of not being thorough. –  Eric Tressler Sep 11 '10 at 16:33
You could also just cite a well-known text book in the area that explains the method. I'm sure the power method is explained in many numerical linear algebra books, like Golub and Van Loan, for example. –  Robin Kothari Sep 11 '10 at 16:44
I've heard someone refer to it as Jacobi's method, so it may be very old. –  Felipe Voloch Sep 11 '10 at 18:09
It is probably more useful to your readers if you cite it in a standard textbook or two, rather than the original paper of Jacobi (or whatever). –  Gerald Edgar Sep 12 '10 at 1:45
I had to cite it in a paper recently (well, orthogonal iteration in fact), and I went for Golub-Van Loan, too. If I were a reader that does not know the power method, I'd rather see a reference to a standard textbook than to a 1910 paper in German. –  Federico Poloni Nov 5 '10 at 8:38

Several researchers indicate that the power iteration method dates back to Herman Müntz. According to the survey aricle "Eigenvalue computation in the 20th century" by Golub and van der Vorst,

Householder called this Simple Iteration, and attributed the first treatment of it to Müntz (1913). Bodewig attributes the power method to von Mises, and acknowledges Müntz for computing approximate eigenvalues from quotients of minors of the explicitly computed matrix $A^k$ , for increasing values of $k$.

Ortiz and Pinkus also mention in "Herman Müntz: A Mathematician’s Odyssey" that

In 1913 he published two notes in Comptes Rendus in connection with the use of iterative techniques for the solutions of algebraic equations. It is very possible that Müntz was the first to develop an iterative procedure for the determination of the smallest eigenvalue of a positive definite matrix. It certainly predates the more generally quoted result of R. von Mises of 1929.

The relevant papers by Müntz:

• Solution directe de l’équation séculaire et de quelques problèmes analogues transcendants, C. R. Acad. Sci. Paris, 156 (1913), 43-46.

• Sur la solution des équations séculaires et des équations intégrales, C. R. Acad. Sci. Paris, 156 (1913), 860-862.

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