Shift Strategy for Non-overdamped Quadratic Eigen-problems

[摘要] In this paper we study properties of non-overdamped quadratic eigen problems. For the non-overdamped Eigen-value problems we cannot apply variational characterization in full. One of the subintervals of the interval in which we can apply variational characterization for Eigen-values of a negative type is known. In this paper we expand this subinterval by giving better right boundry of the variational characterization interval. This is achieved by getting bigger lower boundary for δ+. New strategy is seen in fact that we join suitably selected hyperbolic quadratic pencil to non-overdamped quadratic pencil. From the variational characterization of the hyperbolic eigenproblem we get better lower boundary for δ+.

[关键词] Non-overdamped;Quadratic Eigen-problem;Hyperbolic Quadratic Eigen-problem;Varitional characterization;Quadratic pencil;Rayleigh functional;Shift strategy