“Norm Subsidiarity” or “Norm Diffusion”?

Robust norm equivalencies for diffusion problems

Additive multilevel methods offer an efficient way for the fast solution of large sparse linear systems which arise from a finite element discretization of an elliptic boundary value problem. These solution methods are based on multilevel norm equivalencies for the associated bilinear form using a suitable subspace decomposition. To obtain a robust iterative scheme, it is crucial that the const...

Negative norm stabilization of convection-diffusion problems

We consider a model convection-diiusion problem in the convection-dominated regine. A functional setting is given for stabilized Galerkin approximations, in which the stabilizing terms are based on inner products of the type H ?1=2. These are explicitly computable via multiscale decompositions such as hierarchical nite elements or wavelets (while classical SUPG or Galerkin/least-squares methods...

Amemiya Norm Equals Orlicz Norm in General*

We present a proof that in Orlicz spaces the Amemiya norm and the Orlicz norm coincide for any Orlicz function ‘p. This gives the answer for an open problem. We also give a description of the Amemiya type for the Mazur-Orlicz F-norm.

Rank, Trace-Norm and Max-Norm

We study the rank, trace-norm and max-norm as complexity measures of matrices, focusing on the problem of fitting a matrix with matrices having low complexity. We present generalization error bounds for predicting unobserved entries that are based on these measures. We also consider the possible relations between these measures. We show gaps between them, and bounds on the extent of such gaps.

The Norm Game - How a Norm Fails