Inverse iteration for the quadratic eigenvalue problem

Abstract

The inverse iteration method for the linear eigenvalue problem is extended to the quadratic eigenvalue problem based on the famous Newtonian iteration for algebraic equations. The process is shown to converge to the desired modes by means of a newly introduced continuation parameter for highly non-conservative systems. Only physical co-ordinates are involved and the sparsity of the original matrices is preserved to achieve high computational efficiency. The required orthonormalization condition and the generalized Rayleigh's Quotient are given. The method can handle complex eigensolution without difficulties.