【摘要】 设A=（?）是一m×n阶矩阵,A₁是m阶方阵.当perC[G_c（A₁）]=,2,3,4时,本文给出了解线方程组AX=C的一种算法.G_c（A）是矩阵A的伴随有向图（Coates图）,C[G_C（A）]是图G_C（A）的邻接矩阵.此算法将高斯消元过程直接在G_C（A）上进行,省去了化A为某种标准形的麻烦.此算法显示了对大型稀疏方程是有效的,因此时C[G_C（A）]的积和式perC[G_C（A）]往往较小.Bengt Aspall和Yossi Shiloach对系数矩阵A的每行仅含至多两个非零元时的情形给出了解AX=C的一个特殊的图算法.本文给出的算法包容了这一特殊情况.更多还原

【Abstract】 Let A= (A1A2) be a matrix of degree m×n, A1 a square matrix of degree m, Inthis paper, we give an algorithm to solve the linear equations AX=C provided perC[Gc(A1)] = 1, 2, 3 or 4, where GC(A) denotes the adjacency matrix of graph GC(A). This algorithm carries out the Gaussian elimination directly to GC(A) without finding the canonical form of A. It shows that this algorithm is efficient for sparse equations of large scale for the permanent of C[GC(A)] is, often small.B. Aspall and Y. Shiloach give a graphic algorithm to solve AX=C in the case that each row of matrix A contains at most two nonzero entries. The algorithm inthis paper implies this result as a special case.更多还原