The inclusion principle provides a qualitative characterization of the eigenvalues of a matrix. The principle has been shown to apply to systems described by a single Hermitian matrix, the most important of which being the real symmetric matrix. Self‐adjoint distributed systems, when discretized by either the classical Rayleigh‐Ritz method or by the finite element method, lead to algebraic eigenvalue problems described in terms of two real symmetric matrices. The algebraic eigenvalues problem derived by the classical Rayleigh‐Ritz method possesses the embedding feature required by the inclusion principle, but that derived by the finite element method in general does not. This paper demonstrates that the inclusion principle can be extended to discretized systems derived by the hierarchical finite element method.
|Original language||English (US)|
|Number of pages||11|
|Journal||International Journal for Numerical Methods in Engineering|
|State||Published - Feb 1983|
ASJC Scopus subject areas
- Numerical Analysis
- Applied Mathematics