The well knownChargeSimulation Method, which is commonly used for electric field calculations, is shown to be a particular and ill-conditioned case of the Least Squares Charge Simulation Method. By solving a practical problem, it is shown how to efficiently handle a least squares problem, thus obtaining results of higher precision if compared to the traditionalChargeSimulation Method. For the solution of the resulting linear system, several mathematical methods are analyzed and compared, being stated that the optimum combination of higher precision, lesser error propagation, lesser CPU time and lesser computer RAM are simultaneously reached when applying the Least Squares Charge Simulation Method, solved with the OR decomposition and Householder transformations.12197102Singer, H., Steinbigler, H., Weiß, P., A charge simulation method for high voltage fields (1974) IEEE Transactions on Power Apparatus and Systems, 93, pp. 1660-1668Chow, Y.L., Charalambous, C., Static-field computations by the method of optimized simulated charges (1979) IEE Proceedings, 126 (1), pp. 123-125. , JanuaryAnis, H., Zeitoun, A., El-Ragheb, M., El-Desouki, M., Field calculations around non standard electrodes using regression and their spherical equivalence (1977) IEEE Transactions on Power Apparatus and Systems, 96, pp. 1721-1730Steinbigier, H., Combined application of finite element method and charge simulation method for the computation of electric fields (1979) 3rd International Symposium on High Voltage Engineering, , section 11-11. AugustHoffmann, J.N., Pulino, P., New developments on the combined application of charge simulation and numerical methods for the computation of electric fields (1994) IEEE Summer MeetingBeasley, M.D.R., Comparative study of three methods for computing electric fields (1979) IEE Proceedings, 126 (1), pp. 126-134. , JanuaryMalik, N.H., A review of the charge simulation method and its applications (1989) IEEE Transactions on Electrical Insulation, 24, pp. 3-20. , FebruaryGolub, G.H., Van Loan, C.F., (1985) Matrix Computations, , Baltimore, The John Hopkins University PressNoble, B., Daniel, J., (1977) Applied Linear Algebra, , New Jersey, Prentice HallForsythe, G.E., Moler, C.B., (1967) Computer Solution of Linear Algebraic Systems, , New Jersey, Prentice HallForsythe, C.E., Malcolm, M.A., Moler, C.B., (1977) Computer Methods for Mathematical Computations, , New Jersey, Prentice HallDongarra, J.J., (1979) Unpack User's Guide, , Philadelphia, Society for Industrial and Applied MathematicsSonneweld, P., CGS, a fast Lanczos-type solver for non symmetric linear systems (1989) Siam J. Sci. Stat. Comput., 10 (1), pp. 36-52. , January