Browsing by Subject "point spectrum"

Now showing 1 - 3 of 3

Access status: Open Access ,
Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvalues of finite submatrices
(2007) Malejki, Maria
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space $l^2(\mathbb{N})$ by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator is bounded from below with compact resolvent. In our research we estimate the asymptotics (with $n\to \infty$) of the joint error of approximation for the first n eigenvalues and eigenvectors of the operator by the eigenvalues and eigenvectors of the finite submatrix of order $n \times n$. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in . We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
Access status: Open Access ,
Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices
(2010) Malejki, Maria
The research included in the paper concerns a class of symmetric block Jacobi matrices. The problem of the approximation of eigenvalues for a class of a self-adjoint unbounded operators is considered. We estimate the joint error of approximation for the eigenvalues, numbered from $1$ to $N$, for a Jacobi matrix $J$ by the eigenvalues of the finite submatrix $J_{n}$ of order $pn \times pn$, where $N = \max \{k \in \mathbb{N}: k \leq rpn\}$ and $r \in (0,1)$ is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of $J$ in the case $p = 3$.
Access status: Restricted ,
Asymptotyka widma punktowego dla blokowych macierzy Jacobiego
(Data obrony: 2018-12-17) Jaskuła, Tomasz
Wydział Matematyki Stosowanej