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- W2036940585 abstract "Abstract: Motivated in part by a problem of combinatorial optimization and in part by analogies with quantum computations, we consider approximations of orthogonal matrices U by “non-commutative convex combinations”A of permutation matrices of the type A = ∑ Aσσ, where σ are permutation matrices and Aσ are positive semidefinite n× n matrices summing up to the identity matrix. We prove that for every n×n orthogonal matrix U there is a non-commutative convex combination A of permutation matrices which approximates U entry-wise within an error of cn− 1 2 lnn and in the Frobenius norm within an error of c lnn. The proof uses a certain procedure of randomized rounding of an orthogonal matrix to a permutation matrix." @default.
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- W2036940585 date "2006-01-01" @default.
- W2036940585 modified "2023-10-01" @default.
- W2036940585 title "Approximating Orthogonal Matrices by Permutation Matrices" @default.
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- W2036940585 doi "https://doi.org/10.4310/pamq.2006.v2.n4.a3" @default.
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