Week 3 (Oct 23)

Long Chen. X-Z identity for successive subspace correction method.

ABSTRACT: We shall report a sharp estimate of the convergence rate of multgird methods. Indeed it is an identity on the contraction number for general successive subspace correction methods. The main reference is

[1] J. Xu and L. Zikatanov. The method of alternating projections and the method of subspace corrections in Hilbert space. Journal of The American Mathematical Society, 15:573–597, 2002.

We shall give a simple proof for a special but the most important case of this identity. It will be our basic tools for the analysis of multigrid on adapted grids.