On the inverse of generalized λ‐matrices with singular leading term
Ney Augusto Dumont · International Journal for Numerical Methods in Engineering · 2005
Abstract An algorithm is introduced for the inverse of a λ‐matrix given as the truncated series A0−iλA1−λ2A2+iλ3A3+λ4A4+···+O(λn+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 λ‐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 ω. Copyright © 2005 John Wiley & Sons, Ltd.