In this note we answer two open questions on the finite-dimensional approximation of linear operators in Banach spaces. The first result establishes bounds on the ratio a of the error of adaptive approximations to the error of nonadaptive approximations of linear operators (see [PW], open problem 1); terms are defined more precisely below. This result is of interest partly because of its connec...

In this paper we show how to spatially discretize a distributed model of a piezoelectric beam representing the dynamics of an inflatable space reflector in port-Hamiltonian (pH) form. This model can then be used to design a controller for the shape of the inflatable structure. Inflatable structures have very nice properties, suitable for aerospace applications, e.g., inflatable space reflectors...

We establish a correspondence between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings. As an application, we show that if the underlying field has positive characteristic, then an abelian regular subgroup has finite exponent if the vector space is finite-dimensional, while it can be to...

Numerical simulation of three-dimensional (3D) seismic wavefields forms the basis research on migration methods 3D data based wave equations. Because precision wavefield extrapolation determines imaging accuracy to a certain extent, it is very important study how enhance forward modeling wavefields. Thus, we build an optimized staggered-grid finite-difference (SFD) method with high two-dimensio...

This paper addresses the problem of obtaining finite dimensional models of distributedparameter systems from measurement data using system identification. The data are used to construct approximations of the solution and the forcing function in a finite dimensional space, which are expressed in terms of a finite element basis. A discrete time model is then identified based on the resulting fini...

The Haagerup norm ‖ · ‖h on the tensor product A ⊗ B of two C∗-algebras A and B is shown to be Banach space equivalent to either the Banach space projective norm ‖ · ‖γ or the operator space projective norm ‖ · ‖∧ if and only if either A or B is finite dimensional or A and B are infinite dimensional and subhomogeneous. The Banach space projective norm and the operator space projective norm are ...

Consider a nonlinear ill-posed operator equation F (u) = y where F is defined on a Banach space X. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data. As shown in the literature, depending on the setting, convergence of the regularized solutions of the finite dimensional problems can be with respect to the stro...