【摘要】 <正> 本文是在文[1]-[10]的基础上,进一步给出Jacobi和Gauss-Seidel迭代法收敛与发散几则新的判定准则,同时也给出了块Jacobi和Gauss-Seidel迭代法收敛新的判定准则。这些判定准则不仅允许Jacobi迭代矩阵B的模大于1,而且极易于检验. 为了讨论问题的需要,引入如下记法:设Jacobi迭代阵B=（bij）,N₁ N₂更多还原

【Abstract】 Let B= (bij) is Jacob: iteration matrix, andWe show that the Jacobi and Gauss-Seidel methods are convergent if B satisfies one of the following conditions:(1) rij<l for each i∈N2, j∈N2,(2) rij<l for each i∈N1, j∈N2,(3) γij≤1 for each i∈N1,j∈N2, With strict inequality for at leasi one i and j, and B is an irreducible matrix.(4) γij≤l for eachi∈N1, j∈N2, With strict inequality for at least one i and 7, and B is an irreducible matrix.(5) B is a non-negative matrix (or non-positive) and C =1/2 (B + BT) satisfies one of (1)- (4).The Jacobi and Gauss-Seidel methods are divergent, if B satisfies oae of the following conditions:(1) γij≥1 for each i∈N1,j∈N2, and B is a non-negative irreducible matrix.(2) γij≥1 for each i∈N1,i∈N2, and B is a non-negative irreducible matrix.(3) μ1=Σ|b1j|≥1,更多还原