# Riccati equation

Friday, May 11, 2018 - 12:00pm - 12:30pm

Minyi Huang (Carleton University)

Mean field game theory has been developed largely following two routes by different researchers. One route, called the direct approach, starts by solving a large-scale game and next derives a set of limiting equations. The second route is to apply mean field approximations and formalize a fixed point problem by obtaining the best response of a representative player. A systematic comparison of the two approaches is generally difficult since in the literature very often each approach is applied under various sufficient conditions.

Wednesday, March 16, 2016 - 11:00am - 11:30am

Mark Opmeer (University of Bath)

For discretizations of partial differential equations, the standard methods for numerically solving Lyapunov and Riccati equations (as for example implemented in matlab) are usually not suitable since the computational effort and storage requirements are too high. Analysis of the underlying partial differential equation shows that often good low rank approximations to the exact solution of the Lyapunov or Riccati equation exist. Such low rank approximations are cheap to store and can often be efficiently computed.