A Comparison of Algorithms for the Exact Solution of Linear Equations.

摘要

A computing time study of several algorithms for the exact solution of systems of linear equations with integer or polynomial coefficients is presented. The analytical computing times for rational gauss elimination,exact division elimination (one-step and two-step),and the modular algorithm are summarized and supplemented. Extensive empirical studies illustrate the superiority of the modular algorithm in agreements with the analytical results. All algorithms were programmed in FORTRAN 4for the SAC-1System and all cases were run on a UNIVAC 1108. (Author)