Research On A Matrix Inverse Problem In Structural Dynamic Model Updating

In this paper, we mainly study the centro-symmetic solution of the inverse quadratic eigenvalue problem and its optimal pproximation. Let A=(αij),We called A is a centro-symmetic matrix whenαij=αn+1-i,n+1-j,i,j=1,2,...,n,The inverse eigenvalue problem is to construct centro-symmetic matries M, C and K of sizn n for the quadratic pencil Q(λ)=λ2M+λC+M so that the Q(λ) has a prescribed subset of eigenvalues and eigenvetors. It is shown that the problem is solvable and a iterative algorithms to solve this question is provided.Under some suitable conditions, we give the convergence results. The optimal approximation problem is dicussed and the expression is provided. Numerical results show that the new methods are very effective.