We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded Lipschitz domain Ω in R for d ≥ 2 with piecewise smooth boundary. For piecewise polynomial ansatz spaces and d ∈ {2, 3}, the inverse estimates are explicit in both the local mesh width and the approximation order. An application to efficiency estimates in a ...

The inverse optimization problem is to modify the weight (or cost, length, capacity and so on) such that a given feasible solution becomes an optimal solution. In this paper, we consider the inverse min–max spanning tree problem under the weighted sum-type Hamming distance. For the model considered, we present its combinatorial algorithm that runs in strongly polynomial times. c © 2007 Elsevier...

We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials—given by a list of coefficients in binary—can be computed to a given accuracy by a uniform TC algorithm (a uniform family of constant-depth polynomial-size threshold circuits). The basic idea is to compute the inverse function of the polynomial by a power series. We also discuss an ...

Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2-dimensional inverse discrete Fourier transform, which generalizes the Mattson–Solomon polynomial for Reed–Solomon codes. We also generalize the workings of the generator polynom...

The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical consistency and reconstruction problems for two directions in discrete tomography can be solved in polynomial time, it turns out that these window constraints cause va...