A Padé approximate linearization algorithm for solving the quadratic eigenvalue problem with low‐rank damping

The low‐rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low‐rank damping property, we propose a Padé approximate linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only n + ?m, which is generally substantially smaller than the dimension 2n of the linear eigenvalue problem produced by a direct linearization approach, where n is the dimension of the quadratic eigenvalue problem, and ? and m are the rank of the damping matrix and the order of a Padé approximant, respectively. Numerical examples show that by exploiting the low‐rank damping property, the PAL algorithm runs 33–47% faster than the direct linearization approach for solving modest size quadratic eigenvalue problems. Copyright © 2015 John Wiley & Sons, Ltd.