Browsing by Subject "asymptotics"
Now showing 1 - 8 of 8
- Results Per Page
- Sort Options
Item type:Article, Access status: Open Access , Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvalues of finite submatrices(2007) Malejki, MariaWe 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.Item type:Article, Access status: Open Access , Asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations(2014) Bohner, Martin; Grace, Said R.; Sultana, NasrinIn this paper, we establish some new criteria on the asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations on time scales.Item type:Article, Access status: Open Access , Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices(2010) Malejki, MariaThe 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 $p = 3$.Item type:Article, 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, LechWe 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.Item type:Thesis, Access status: Restricted , Metody bootstrapowe w problemie Wicksella(Data obrony: 2015-07-02) Sierpiński, Damian
Wydział Matematyki StosowanejItem type:Thesis, Access status: Restricted , Model dwumianowy z szybką asymptotyką do modelu Blacka-Scholesa(Data obrony: 2014-09-15) Borek, Justyna
Wydział Matematyki StosowanejItem type:Thesis, Access status: Restricted , Nierówności dla wybranych wartości własnych pewnych klas macierzy symetrycznych(Data obrony: 2015-06-26) Kozioł, Wojciech
Wydział Matematyki StosowanejItem type:Article, Access status: Open Access , One boundary value problem including a spectral parameter in all boundary conditions(Wydawnictwa AGH, 2023) Kabataş, AyşeIn this paper, asymptotic formulae for solutions and Green's function of a boundary value problem are investigated when the equation and the boundary conditions contain a spectral parameter.