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Boundary element discretizations of surface and hybrid surface/volume formulations of electromagnetic scattering problems generate large and dense systems of linear equations that are tough to solve by iterative techniques. The restarted generalized minimal residual (GMRES) method is virtually always used when the systems are non-Hermitian and indefinite. However, it may be prohibitively expensive especially for large scale out-of-core integral codes. We present experiments with a novel class of iterative methods that have constant, low memory and algorithmic cost per iteration. The results on some selected matrix problems arising from realistic radar-cross-section calculation indicate that the new family of algorithms is amazingly competitive with the most popular iterative techniques in use today for solving linear systems.