組合せグラフによる消去法のグラフ表現

概要

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A graphical approach to solving simultaneous equations was tried in a previous paper by a signal flow graphical representation of elimination. In this paper, elimination is characterized by "combinatorial graphs" , which are defined as the graphs consisting of a set of points with "coordinates" and a set of branches with "coefficients". The "coordinates" of points are given by combinations of suffices corresponding to equations, and the "coefficient" of a branch between two points is given by a definite operation concerning the "coordinates" of these points. A signal flow graph called "elimination graph" is obtained from a graphical representation of elimination on the combinatorial graph associated with a given system of equations. The elimination graph connected to a graph of equations gives a solution of the equations, and also gives a graphical method for computing the determinant related to the coefficients of the equations.
長崎大学工学部,Faculty of Engineering, Nagasaki Universityの論文