Guaranteed lower bounds for eigenvalues

Guaranteed lower bounds for eigenvalues

This paper introduces fully computable two-sided bounds on the eigenvalues of the Laplace operator on arbitrarily coarse meshes based on some approximation of the corresponding eigenfunction in the nonconforming Crouzeix-Raviart finite element space plus some postprocessing. The efficiency of the guaranteed error bounds involves the global mesh-size and is proven for the large class of graded m...

Schrödinger secant lower bounds to semirelativistic eigenvalues

It is shown that the ground-state eigenvalue of a semirelativistic Hamiltonian of the form H = √ m2 + p2+V is bounded below by the Schrödinger operator m+βp2+V, for suitable β > 0. An example is discussed.

Guaranteed lower eigenvalue bounds for the biharmonic equation

The computation of lower eigenvalue bounds for the biharmonic operator in the buckling of plates is vital for the safety assessment in structural mechanics and highly on demand for the separation of eigenvalues for the plate’s vibrations. This paper shows that the eigenvalue provided by the nonconformingMorley finite element analysis, which is perhaps a lower eigenvalue bound for the biharmonic...

Some Lower Bounds for Estrada Index

Lower Bounds for Eigenvalues of Schatten-von Neumann Operators

Let Sp be the Schatten-von Neumann ideal of compact operators equipped with the norm Np(·). For an A ∈ Sp (1 < p <∞), the inequality [ ∞ ∑ k=1 |Reλk(A)| ] 1 p + bp [ ∞ ∑ k=1 | Imλk(A)| ] 1 p ≥ Np(AR)− bpNp(AI) (bp = const. > 0) is derived, where λj(A) (j = 1, 2, . . . ) are the eigenvalues of A, AI = (A − A∗)/2i and AR = (A + A∗)/2. The suggested approach is based on some relations between the ...