A new efficient solution method for a system of linear equations: Partially Solving Method (PSM)

We present a new method of solving a system of linear equations, called Partially Solving Method (PSM). The PSM can essentially deal with only a subsystem at each processing stage without complete knowledge of the entire system. For dense systems, it reduces the necessary memory space effectively by a factor of four as compared with the conventional LU-decomposition method. For sparse systems, the method operates up to, twice as fast as Gaussian elimination method, and the efficiency in both space and time is further enhanced by a proper ordering of selections of the equations. It may be feasible to apply the PSM in a parallel processing environment, when the entire system is divided into subsystems.