广义Jacobi矩阵的逆问题  

The inverse problem of a generalized Jacobi matrix

作　　者：艾树利[1] 

机构地区：[1]长安大学数学与信息科学系,陕西西安710064

出　　处：《纺织高校基础科学学报》2008年第2期211-215,共5页Basic Sciences Journal of Textile Universities

摘　　要：考虑加权型Jacobi矩阵的逆问题.基于逐层递退方法,通过特征对给出Jacobi矩阵存在和惟一的充分必要条件,并由特征对构造出此Jacobi矩阵.即当i=1,2,…,k-1时,如果Di≠0且[(μ1-λ)di+λqiDi+(1μ-λ)Mi-1+(1μ-λ)qixiyi+1]/Di>0,那么bi=[(μ1-λ)di+λqiDi+(1μ-λ)Mi-1+(1μ-λ)qixiyi+1]/Di,若Di=0,bi=(μ1qi-1yi-1+μ1qiyi+1-bi-1yi-1)/yi+1,且ai为任意实数.对于i=k,k+1,…,n-1,ai,bi可类似求得.The inverse problem of weighted Jacobi matrices was considered. Based on gradually discussion, in terms of eigenpairs, a necessary and sufficient condition is given so that the solution of the generalized inverse problem of a Jacobi matrix is determined uniquely and the Jacobi matrix is constructed from its generalized eigenpairs. That is,when i=1,2,…,k-1,if Di≠0,[（μ1-λ）di＋λqiDi＋（μ1-λ）Mi-1＋（μ1-λ）qixiyi＋1]/Di〉0,then bi=[（μ1-λ）di＋λqiDi＋（μ1-λ）Mi-1＋（μ1-λ）qoxiyi＋1]/Di,ai={λpi＋[λqi-1-bi-1）xi-1＋（λqi-bi）xi＋1]/xi,xi≠0,/μipi＋[（μ1qi-1-bi-1）yi-1＋（μ1qi-bi）/yi＋1]/yi,xi=0.If Di=0,bi=（μ1qi-1yi-1＋μ1qiyi＋1-bi-1yi-1）/yi＋1, and ai can be any real number.For i=k,k＋1,…,n-1,ai,bi can be calculated similarly,

关 键 词：JACOBI矩阵 广义逆问题 正定矩阵 

分 类 号：O177.7[理学—数学]