计算物理 ›› 1994, Vol. 11 ›› Issue (4): 451-456.
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戴华
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Dai Hua
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摘要: 研究如下一类Jacobi矩阵特征值反问题:问题IEP:给定两个互异实数λ,μ(λ<μ)和两个n维非零实向量x,y,求n阶Jacobi矩阵J,使得(λ,x),(μ,y)分别恰是J的第i,j(i≠j)个特征对。还分析了Jacobi矩阵的特征性质,给出了一个特征对恰是Jacobi矩阵J的第i个特征对的充分必要条件,由此导出了问题IEP有解的充分必要条件。
关键词: 特征值, 特征向量, 反问题, Jacobi矩阵
Abstract: The following inverse eigenvalue problem for Jacobi matrices is considered: Problem IEP.Given λ,μ∈R(λ<μ and x,y∈Rn,x≠0,y≠0, find n×n Jacobi matrix J such that (λ,x) and (μ,y) are exactly the i-th and j-th (i≠j) eigenpairs of the Jacobi matrix J, respectively. The eigenanalysis of Jacobi matrices is given. The necessary and sufficient condition is obtained for one eigenpair to be exactly the i-th eigenpair of a Jacobi matrix. Some necessary and sufficient conditions for existence of solution of the Problem IEP are given.
Key words: characteristic value, characteristic vector, inverse problem, Jacobi matrix
中图分类号:
O241.6
戴华. Jacobi矩阵特征值反问题[J]. 计算物理, 1994, 11(4): 451-456.
Dai Hua. INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 11(4): 451-456.
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