Abstract:In this report, I will introduce the semi-group formulation of the SPDE. And I shall give a stability analysis for filtering algorithm based on spectral methods from two aspects.1. Asymptotic analysis of the relationship between the number of spectra and errors in spectral methods.2. Analysis of the stability of spectral algorithm by time discretization
IntroductionThis course is an introduction to the convergence and collapsing theory of Riemannian manifolds, which is an important tool in Riemannian geometry. We shall introduce the Gromov-Hausdorff distance and study the convergence theory of Riemannian manifolds with respect to this distance. We will discuss the collapsing theory of Riemannian manifolds with bounded sectional curvatures.Lect...