Dynamic regularization of input estimation problems by explicit block inversion

Input estimation problems in structural dynamics often lead to solving damped least squares problems. Explicit block inversion algorithms are developed to invert the associated upper block triangular Toeplitz matrix. Moreover, the derived inversion algorithms enable the introduction of a new type of sequential regularization technique. For optimal regularization parameters, it is demonstrated by a numerical example that the solution using the proposed regularization technique has an upper bound equal to zeroth-order Tikhonov regularization.