Deflation techniques for computational electromagnetism, Part I: Theoretical considerations

The deflation technique replaces small eigenvalues of a matrix with zeros to accelerate convergence of iterative linear solvers. In this paper, it is shown that the reason why recently proposed computational frameworks such as the explicit and implicit error corrections and singularity decomposition as well as the conventional AV method improve convergence in linear solvers is clarified from a view point of the matrix deflation.