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2013 Spectral characterization for von Neumann's iterative algorithm in $\mathbb{R}^n$
Rudy Joly, Marco López, Douglas Mupasiri, Michael Newsome
Involve 6(2): 243-249 (2013). DOI: 10.2140/involve.2013.6.243


Our work is motivated by a theorem proved by von Neumann: Let S1 and S2 be subspaces of a closed Hilbert space X and let xX. Then

lim k ( P S 2 P S 1 ) k ( x ) = P S 1 S 2 ( x ) ,

where PS denotes the orthogonal projection of x onto the subspace S. We look at the linear algebra realization of the von Neumann theorem in n. The matrix A that represents the composition PS2PS1 has a form simple enough that the calculation of limkAkx becomes easy. However, a more interesting result lies in the analysis of eigenvalues and eigenvectors of A and their geometrical interpretation. A characterization of such eigenvalues and eigenvectors is shown for subspaces with dimension n1.


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Rudy Joly. Marco López. Douglas Mupasiri. Michael Newsome. "Spectral characterization for von Neumann's iterative algorithm in $\mathbb{R}^n$." Involve 6 (2) 243 - 249, 2013.


Received: 31 May 2012; Accepted: 2 June 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1275.41041
MathSciNet: MR3096371
Digital Object Identifier: 10.2140/involve.2013.6.243

Primary: 41A65
Secondary: 47N10‎

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.6 • No. 2 • 2013
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