论文标题
广义逆特征值问题和$ M $ functions
A generalized inverse eigenvalue problem and $m$-functions
论文作者
论文摘要
在此手稿中，考虑了一个涉及线性铅笔$（Z \ Mathcal {J} _ {[0，n]} - \ Mathcal {h} _ {[0，n]}）$的矩阵理论中的矩阵理论中产生的矩阵的$（z \ Mathcal {j} _ {[0，n]} - 除了重建Hermitian矩阵$ \ MATHCAL {h} _ {[0，n]} $的条目$ b_j的$，还提供了有理函数的特征，这些功能是规定的eigenVectors的组成部分。关于$ \ Mathcal {J} _ {[0，n]} $的正定义的条件，并且通常也是直接问题中的假设。此外，通过铅笔$（z \ Mathcal {j} _ {[0，n]} - \ Mathcal {h} _} _ {[h} _ {[0，n]} $，$ m $ $ m $ m m $ m m $ - m m $ m m- m m- m m-- funcctions。
In this manuscript, a generalized inverse eigenvalue problem is considered that involves a linear pencil $(z\mathcal{J}_{[0,n]}-\mathcal{H}_{[0,n]})$ of matrices arising in the theory of rational interpolation and biorthogonal rational functions. In addition to the reconstruction of the Hermitian matrix $\mathcal{H}_{[0,n]}$ with the entries $b_j's$, characterizations of the rational functions that are components of the prescribed eigenvectors are given. A condition concerning the positive-definiteness of $\mathcal{J}_{[0,n]}$ and which is often an assumption in the direct problem is also isolated. Further, the reconstruction of $\mathcal{H}_{[0,n]}$ is viewed through the inverse of the pencil $(z\mathcal{J}_{[0,n]}-\mathcal{H}_{[0,n]})$ which involves the concept of $m$-functions.
