Abstract
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.
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References
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Osano, M., Nakajima, K. & Tanimoto, M. A new efficient solution method for a system of linear equations: Partially Solving Method (PSM). Japan J. Indust. Appl. Math. 13, 243–256 (1996). https://doi.org/10.1007/BF03167246
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DOI: https://doi.org/10.1007/BF03167246