ISSN:
1070-5325
Keywords:
nearest doubly stochastic matrix
;
alternating projections
;
first moment
;
normal cone
;
RC1
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
Let T be an arbitrary n × n matrix with real entries. We consider the set of all matrices with a given complex number as an eigenvalue, as well as being given the corresponding left and right eigenvectors. We find the closest matrix A, in Frobenius norm, in this set to the matrix T. The normal cone to a matrix in this set is also obtained. We then investigate the problem of determining the closest ‘doubly stochastic’ (i.e., Ae = e and eT A = eT, but not necessarily non-negative) matrix A to T, subject to the constraints ${\bf e}_{1}^{\rm T} A^{k} {\bf e}_{1} = {\bf e}_{1}^{\rm T}T^{k}{\bf e}_{1}$, for k = 1, 2, … A complete solution is obtained via alternating projections on convex sets for the case k = 1, including when the matrix is non-negative. Copyright © 1999 John Wiley & Sons, Ltd.
Type of Medium:
Electronic Resource
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