The nearness problems for symmetric centrosymmetric with a special submatrix constraint |
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Authors: | Jiao-Fen Li Xi-Yan Hu Lei Zhang |
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Institution: | 1.School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin,Peoples Republic of China;2.College of Mathematics and Econometrics,Hunan University,Hunan,People’s Republic of China |
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Abstract: | We say that X=xij]i,j=1nX=x_{ij}]_{i,j=1}^n is symmetric centrosymmetric if x
ij
= x
ji
and x
n − j + 1,n − i + 1, 1 ≤ i,j ≤ n. In this paper we present an efficient algorithm for minimizing ||AXA
T
− B|| where ||·|| is the Frobenius norm, A ∈ ℝ
m×n
, B ∈ ℝ
m×m
and X ∈ ℝ
n×n
is symmetric centrosymmetric with a specified central submatrix x
ij
]
p ≤ i,j ≤ n − p
. Our algorithm produces a suitable X such that AXA
T
= B in finitely many steps, if such an X exists. We show that the algorithm is stable any case, and we give results of numerical
experiments that support this claim. |
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Keywords: | |
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