Browsing by Subject "tridiagonal matrix"

Now showing 1 - 7 of 7

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: Open Access ,
Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices
(Wydawnictwa AGH, 2020) Harrat, Ayoub; Zerouali, El Hassan; Zieliński, Lech
We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.
Access status: Open Access ,
Asymptotics of the discrete spectrum for complex Jacobi matrices
(2014) Malejki, Maria
The spectral properties and the asymptotic behaviour of the discrete spectrum for a special class of inﬁnite tridiagonal matrices are given. We derive the asymptotic formulae for eigenvalues of unbounded complex Jacobi matrices acting in $l^2(\mathbb{N})$.
Access status: Restricted ,
Macierze odwrotne dla macierzy trójdiagonalnych
(Data obrony: 2015-10-30) Kustra, Magda
Wydział Matematyki Stosowanej
Access status: Restricted ,
Własności macierzy trójdiagonalnych
(Data obrony: 2018-07-11) Such, Karolina
Wydział Matematyki Stosowanej
Access status: Restricted ,
Wzory analityczne na funkcje charakterystyczne i wektory własne dla pewnych klas skończonych macierzy Jacobiego
(Data obrony: 2013-07-16) Laskoś, Mariusz
Wydział Matematyki Stosowanej