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We introduce a novel variant of the Lanczos method for computing a few eigenvalues of sparse and/or dense non-Hermitian systems arising from the discretization of Maxwell-or Helmholtz-type operators in electromagnetics. We develop a Krylov subspace projection technique built upon short-term vector recurrences that does not require full reorthogonalization and can approximate simultaneously both left and right eigenvectors. We report on experiments for solving eigenproblems arising in thedoi:10.2528/pier10072204 fatcat:pdyiafjl3rhzjbqr7midd74d5m