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广义Jacobi矩阵的逆问题

The inverse problem of a generalized Jacobi matrix
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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,
作者 艾树利
出处 《纺织高校基础科学学报》 CAS 2008年第2期211-215,共5页 Basic Sciences Journal of Textile Universities
关键词 JACOBI矩阵 广义逆问题 正定矩阵 Jacobi matrix generalized inverse problem positive definite matrix
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参考文献7

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