Related papers: Computation of volume potentials over bounded doma…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…
In the present article, the volume of the hypersphere in n-dimensional euclidean space is recalculated in a rather original way by using the theory of generalized functions (tempered distributions). The calculation is performed by applying…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the…
We study the properties of the maximal volume $k$-dimensional sections of the $n$-dimensional cube $[-1,1]^n$. We obtain a first order necessary condition for a $k$-dimensional subspace to be a local maximizer of the volume of such…
Some difficulties, both numerical and conceptual, of the method to compute one dimensional wave functions by numerically integrating the quantum Hamilton-Jacobi equation, presented in the paper mentioned in the title, are analyzed. The…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
We analyse the maximum achievable rate of sustained computation for a given convex region of three dimensional space subject to geometric constraints on power delivery and heat dissipation. We find a universal upper bound across both…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the…
The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…
Fundamental limits on communication rates over quantum channels are given by mathematical expressions involving entropic formulas. Often, it is unclear if these expressions are computable. This thesis describes contributions to the study of…
The inverse of an $\infty \times \infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Green's operator…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
We find asymptotically optimal methods of recovery of the integration operator given values of the function at a finite number of points for a class of multivariate functions defined on a bounded star domain that have bounded in $L_p$ norm…
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a…
We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.
From a scalar field defined at the corner of a cube, an isosurface can be extracted using the Marching Cube algorithm. The isosurface separates the cell into two or more partial cells. A similar situation arises when an material interface…
We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic…
We give a very simple approach to the computation of tube volumes of self-similar sprays using a functional equation satisfied by them.