求特征值和特征向量的同伦方法

关于截断移位的扩张特征值和扩张特征向量

On extended eigenvalues and extended eigenvectors of truncated shift

本文给出了定义在模型空间K_u：= H^2 \ominus uH^2上的截断移位的扩充本征向量集的完整描述，其中u是Blaschke积.

Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries

We consider the eigenvalue problem $Ax = λx$ where $A \in \mathbb{R}^{n \times n}$ and the eigenvalue is also real $λ\in \mathbb{R}$. If we are given $A$, $λ$ and, additionally, the absolute value of the entries of $x$ (the vector $(|x_i|)_{i=1}^n$), is there a fast way to recover $x$? In particular, can this be done quicker than computing $x$ from scratch? This may be understood as a special case of the phase retrieval problem. We present a randomized algorithm which provably converges in expectation whenever $λ$ is a simple eigenvalue. The problem should become easier when $|λ|$ is large and…

关于非负矩阵的正特征值和正特征向量

On the positive eigenvalues and eigenvectors of a non-negative matrix

本文在矩阵可数共尾的假设下，给出了题目中各项的一般理论。

Calculating max-eigenvalues and max-eigenvectors with jumps of matrices

The eigenvalue problem for an irreducible non negative matrix $A=[a_{ij}]$ in the max-algebra is the form $A \otimes x = λx$ where $(A \otimes x)_i = \max (a_{ij}x_j), x=(x_1,x_2, \dots, x_n)^t $ and $λ$ refers to maximum cycle geometric mean $μ(A) $. In this paper we exhibit a method to compute $μ(A)$ and max-eigenvector by using mutation of matrices. Since the order of power method algorithm is $O(n^3)$, the advantage of this paper present a faster procedure.

On the eigenstructure of the $(α,q)$-Bernstein operator

We obtain eigenvalues and eigenvectors of the $(α,q)$-Bernstein operator $T_{n,q,α}$. Moreover, we will give the limit behaviour of these eigenvalues and eigenvectors for all $q.$