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Spectral
characterization for von Neumann's iterative algorithm in
$\mathbb{R}^n$
Rudy Joly, Marco López, Douglas Mupasiri and Michael Newsome
Vol. 6 (2013), No. 2, 243–249
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Abstract |
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Our work is motivated by a theorem proved by von Neumann: Let and be subspaces of a closed Hilbert space and let . Then where denotes the orthogonal projection of onto the subspace . We look at the linear algebra realization of the von Neumann theorem in . The matrix that represents the composition has a form simple enough that the calculation of becomes easy. However, a more interesting result lies in the analysis of eigenvalues and eigenvectors of and their geometrical interpretation. A characterization of such eigenvalues and eigenvectors is shown for subspaces with dimension . |
Keywords
orthogonal projections, von Neumann, best approximations
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Mathematical Subject Classification 2010
Primary: 41A65
Secondary: 47N10
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Milestones
Received: 31 May 2012
Accepted: 2 June 2013
Published: 1 September 2013
Communicated by Jim Haglund
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Authors |
| Rudy Joly | |
| Johns Hopkins University 29 Hillview Avenue Boston, MA 02131 United States |
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| Marco López | |
| Department of Mathematics University of North Texas 1716 W. Hickory St. Apt 2 Denton, TX 76201 United States |
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| Douglas Mupasiri | |
| Department of Mathematics University of Northern Iowa 220 Wright Hall Cedar Falls, IA 50614-0506 United States |
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| Michael Newsome | |
| Jackson State University 8845 Hwy 12 West Sallis, MS 39160 United States |
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