Matrix thinning technique by preconditioning methods and MEI concept

In this summary, a novel matrix thinning technique, matrix sparse decomposition (MSD) technique, has been introduced. The MSD technique, based on the basic concept of measured equation of invariance (MEI) method, i.e., there exist some local relationships between certain physical parameters, has used the least square (LS) technique of preconditioning methods to thin a dense matrix in singular integral equations into two highly sparse matrices. Mathematically speaking, MSD is a new development of the preconditioning methods. From physical point of view, MSD is a new extension of the MEI method. Numerical examples for wire antennas and the scattering of 2-D simple conducting objects show that the high sparse rate of the MSD matrices can be obtained