Shuo Zhang,Institute Computing Technology Chinese Academy of Science
Room 306, No.5 Science Building
For the computation of eigenvalues, high-efficiency comes from high accuracy versus low cost; more information obtained also promotes the efficiency, when, e.g., the upper or lower bound are got known. A basis concept to describe the efficiency is order, for accuracy or cost; a scheme with highest order of accuracy or lowest order of cost ever possible are called optimal. In practical problems, moreover, some more issues besides order are also frequently considered for high efficiency. In this talk, we present some optimal schemes for eigenvalue computation. Speciﬁcally, we consider three features. First, design schemes with optimal computational cost; second, design schemes with optimal computational cost; third, a rigorous comparison between two optimal schemes with same order. The model problems are Poisson equation and biharmonic-type fourth order problems.