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))

作　　者：杜菲[1] 畅大为[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《纺织高校基础科学学报》2013年第4期511-515,共5页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(60671063)

摘　　要：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.

关 键 词：双对角占优矩阵 对角占优矩阵 等对角占优矩阵 ρ(A^-1)下界 

分 类 号：O241.6[理学—计算数学]