TY  - JOUR
ID  - Malejki2010
LB  - Malejki2010
AU  - Malejki, Maria
TI  - Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices
ST  - Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 3
SP  - 311
EP  - 330
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.3.311
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.3.311
AB  - 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 \(p=3\).
KW  - symmetric unbounded Jacobi matrix
KW  - block Jacobi matrix
KW  - tridiagonal matrix
KW  - point spectrum
KW  - eigenvalue
KW  - asymptotics
SN  - 1232-9274
ER  -