Inverse eigenvalue problems and their associated approximation problems for matrices with J-(Skew) Centrosymmetry

摘要

The inverse problems play an important role in MEG reconstructions. Inthis paper, a partially described inverse eigenvalue problem and an associated optimal approximationproblem for J-centrosymmetric matrices are considered respectively. It is shown under whichconditions 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 besolved. The formula of its unique solution is given. Also, the case for J-skew centrosymmetricmatrices is considered.