Talks

We devised an IDR(s)-based SOR method and presented its effectiveness in view of efficiency and robustness by comparison with other iterative methods one year ago. In this talk, we consider the preconditioned IDR(s)-based Residual Reduction (R2) method as an extension of the IDR(s)-based SOR method in view of robust preconditioning. Moreover, we present numerical experiments that clearly show that our proposed IDR(s)-R2 method outperforms other approaches.

Lur'e equations are a generalization of algebraic Riccati equations and they arise in linear-quadratic optimal control with cost functional being singular in the input.
For Riccati equations, it is well-known that there is a one-to-one correspondence between set of solutions and certain Lagrangian eigenspaces of a Hamiltonian matrix.
The aim of this talk is to generalize this concept to Lur'e equations. We are led to the consideration of deflating subspaces of even matrix pencils.

1. A brief introduction about our group in Peking University
2. Seismic design of buildings with accidental eccentricity
3. Structural design of wind turbine blades