Inverse eigenvalue problems and their associated approximation problems for matrices with J-(Skew) Centrosymmetry - Liu Zhongyun (2009)
The inverse problems play an important role in MEG reconstructions. In this paper, a partially described inverse eigenvalue problem and an associated optimal approximation problem for J-centrosymmetric matrices are considered respectively. It is shown under which conditions the inverse eigenproblem has a solution. An expression of its general solution is given. In case a solution of the inverse eigenproblem exists, the optimal approximation problem can be solved. The formula of its unique solution is given. Also, the case for J-skew centrosymmetric matrices is considered.