In this paper we investigate the least eigenvalue of a graph whose complement is connected, and present a lower bound for the least eigenvalue of such graph. We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.

We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is method rectangular generalized problems, which we extend to quasimatrices objects combining matrices. strength approach its flexibility lies in quasimatrix allowing basis functions be chosen arbitrarily, good choice (e.g., those obtained by solving ...

Abstract In this paper we discuss spectral properties of operators associated with the least-squares finite-element approximation elliptic partial differential equations. The convergence discrete eigenvalues and eigenfunctions towards corresponding continuous eigenmodes is studied analyzed help appropriate $L^2$ error estimates. A priori a posteriori estimates are proved.