We study the approximation of spectrum least-squares operators arising from linear elasticity. consider a two-field (stress/displacement) and three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. prove priori estimates we confirm theoretical results simple two-dimensional numerical experiments.

The least-squares method can be used to approximate an eigenvector for a matrix when only an approximation is known for the corresponding eigenvalue. In this paper, this technique is analyzed and error estimates are established proving that if the error in the eigenvalue is sufficiently small, then the error in the approximate eigenvector produced by the least-squares method is also small. Also...

In this paper we get a structural property for a graph having the minimal least eigenvalue among all graphs of fixed order and given chromatic number, and characterize such graphs under the condition that the chromatic number is not larger than half the order of the graph. As a result, we obtain a lower bound on the least eigenvalue in terms of the chromatic number, and an upper bound on the ch...