On the inverse of generalized -matrices with singular leading term

An algorithm is introduced for the inverse of a -matrix given as the truncated series A0 − i A1 − 2A2 + i 3A3 + 4A4 +· · ·+O( n+1) with square coefficient matrices and singular leading term A0. Moreover, A1 may be conditionally singular and no restrictions are made for the remaining terms. The result is a -matrix given as a unique, truncated series of the same error order. Motivation for this problem is the evaluation of the frequency-dependent stiffness matrix of general boundary or macro-finite elements in the frame of a hybrid variational formulation that is based on a flexibility matrix F expressed as a truncated power series of the circular frequency