Premium
Numerical solutions of AXB = C for centrosymmetric matrix X under a specified submatrix constraint
Author(s) -
Li Jiaofen,
Hu Xiyan,
Zhang Lei
Publication year - 2011
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.771
Subject(s) - constraint (computer aided design) , mathematics , combinatorics , matrix norm , norm (philosophy) , matrix (chemical analysis) , algorithm , eigenvalues and eigenvectors , chemistry , geometry , physics , chromatography , quantum mechanics , political science , law
We say that X = [ x ij ] n i, j = 1is centrosymmetric if x ij = x n − j + 1, n − i + 1 , 1⩽ i, j ⩽ n . In this paper, we present an efficient algorithm for minimizing ∥ AXB − C ∥ where ∥·∥ is the Frobenius norm, A ∈ℝ m × n , B ∈ℝ n × s , C ∈ℝ m × s and X ∈ℝ n × n is centrosymmetric with a specified central submatrix [ x ij ] p ⩽ i, j ⩽ n − p . Our algorithm produces a suitable X such that AXB = C in finitely many steps, if such an X exists. We show that the algorithm is stable in any case, and we give results of numerical experiments that support this claim. Copyright © 2011 John Wiley & Sons, Ltd.