A symmetric generalized inverse eigenvalue problem in structural dynamics model updating

Updating an existing but inaccurate structural dynamics model with measured data can be mathematically reduced to the problem of the best approximation to a given matrix pencil in the Frobenius norm under a given spectral constraint and a submatrix pencil constraint. In this paper, a direct method and the associated mathematical theories for solving this problem are proposed. It is shown that the best approximation solution is unique and an explicit expression of the solution is derived. Numerical examples show that the proposed method is quite accurate and efficient.