On the convergence of row-modification algorithm for matrix projections
Hu, Xiaomi Hansohm, Juergen Hoffmann, Linda Zohner, Ye Emma
Hu, Xiaomi
Hansohm, Juergen
Hoffmann, Linda
Zohner, Ye Emma
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2012-02
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Article
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Algorithm,Closed and convex set,Matrix projection,Multivariate isotonic regression
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Hu, X., J. Hansohm, L. Hoffmann, and Y.E. Zohner. 2012. "On the convergence of row-modification algorithm for matrix projections". Journal of Multivariate Analysis. 105 (1): 216-221.
Abstract
This paper proposes an algorithm for matrix minimum-distance projection, with respect to a metric induced from an inner product that is the sum of inner products of column vectors, onto the collection of all matrices with their rows restricted in closed convex sets. This algorithm produces a sequence of matrices by modifying a matrix row by row, over and over again. It is shown that the sequence is convergent, and it converges to the desired projection. The implementation of the algorithm for multivariate isotonic regressions and numerical examples are also presented in the paper. (C) 2011 Elsevier Inc. All rights reserved.
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Elsevier
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Journal of Multivariate Analysis
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0047-259X