一类严格双对角优势矩阵ρ(A^(-1))下界的估计

The estimations of the lower bound of ρ(A^(-1))

研究严格双对角占优矩阵A在一定条件下,ρ(A-1)下界的一种新估计.对满足n≥k≥i≥1的任意k,i,有|akk|-Rk≤|aii|-Ri,进而得到新的下界min i≠j|ajj|+Ri(A)|aii×ajj|-Ri(A)×Rj(A}).并且证明这种新的估计要比已存在的下界更精确.最后用数值例子说明了这个结论的有效性.

The estimations of the lower bound of ρ（A^-1） is discussed when matrix A is under a certain conditions and A is a strictly doubly diagonally dominant matrix. The ｜akk｜-Rk≤laii｜-Ri of every k,i subjected to n≥k≥i≥1 is obtained. Further the new lower bound mini≠j｜｜ajj｜＋Ri（A）/｜aii×ajj｜-Ri（A）×Rj（A）} is received. It is proved that this new estimations is better than the lower existing bound,and the numercial example illustrates the effectiveness of the criteria.