The convergence of the minimal energy interpolatory splines on the unit sphere is studied in this paper. An upper bound on the difference between a sufficiently smooth function and its interpolatory spherical spline in the infinity norm is given. The error bound is expressed in terms of a second order spherical Sobolev-type seminorm of the original function. §

An output least-squares type functional is employed to identify the Lamé parameters in linear elasticity. To be able to identify even the discontinuous Lamé parameters the regularization is performed by the BV-seminorm. Finite element discretization is used and convergence analysis is given. Numerical examples are given to show the feasibility of the approach. c © 2008 Elsevier Ltd. All rights ...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by the first author for a simpler, less isotropic, ...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an “upwind” finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by Chambolle for a simpler, more anisotropic, fin...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by the first author for a simpler, less isotropic, ...

In linear algebra, functional analysis and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to all vectors in a vector space, other than the zero vector. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors. A simple example is the 2-dimensional Euclidean space R 2 equipped with the Euclidean norm. Elements in...

This paper considers the use of the anisotropic total variation seminorm to recover a two dimensional vector x ∈ CN×N from its partial Fourier coefficients, sampled along Cartesian lines. We prove that if (xk,j − xk−1,j)k,j has at most s1 nonzero coefficients in each column and (xk,j − xk,j−1)k,j has at most s2 nonzero coefficients in each row, then, up to multiplication by log factors, one can...

For arbitrary w : R → [0, 1] the general form of the continuous linear functionals on the space C 0 w of all functions f continuous on the real line, lim |x|→+∞ w(x)f (x) = 0 , equipped with seminorm ||f || w := sup x∈R w(x)|f (x)| , is found. The weighted analog of the Weierstrass polynomial approximation theorem and a new version of M.G. Krein's theorem about partial fraction decomposition of...

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex ...

We study the stability in the H1-seminorm of the L2-projection onto finite element spaces in the case of nonuniform but shape regular meshes in two and three dimensions and prove, in particular, stability for conforming triangular elements up to order twelve and conforming tetrahedral elements up to order seven.