Application of the Cramer rule in the solution of sparse systems of linear algebraic equations (Q5948563)

This paper refines the numerical structure approach of \textit{A. Y. Suchkov} [Graphs of gearing morphisms. Leningrad, Quebec (1983)] to find determinants of random unstructured sparse matrices quickly. The determinant of such matrices is computed via a tree algorithm for the non-zero entries in each row which helps determine the nonzero terms in the classical determinant definition. NEWLINENEWLINENEWLINEUltimately this is applied to find solutions to random sparse linear systems via Cramer's rule. The algorithm is compared to the one of finding determinants via digraphs of \textit{W.-K. Chen} [Applied graph theory (1971; Zbl 0229.05107); 2nd rev. ed. (1976; Zbl 0325.05102)], but not to any other direct or iterative method, so that its true worth is unfortunately undocumented.