Related papers: Reconstruction of rough potentials in the plane
We demonstrate a new ultrafast pulse reconstruction modality which is somewhat reminiscent of frequency resolved optical gating but uses a modified setup and a conceptually different reconstruction algorithm that is derived from…
This paper is concerned with function reconstruction from samples. The sampling points used in several approaches are (1) structured points connected with fast algorithms or (2) unstructured points coming from, e.g., an initial random draw…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
We compute the renormalon ambiguity of the static potential, in the limit of a large number of flavors. An extrapolation of the QED result to QCD implies that the large distance behavior of the quark potential is arbitrary in perturbation…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
In this paper we establish square-function estimates on the double and single layer potentials with rough inputs for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper…
We develop reconstruction schemes to determine penetrable obstacles in a region of \mathbb{R}^{2} or \mathbb{R}^{3} and we consider anisotropic elliptic equations. This algorithm uses oscillating-decaying solutions to the equation. We apply…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
For $n>3$, every $n\times n$ partial Cayley matrix with at most $n-1$ holes can be reconstructed by quadrangle criterion. Moreover, the holes can be filled in given order. Without additional assumptions, this is the best possible result.…
Quarkonium resonances in the complex-mass scale are studied. Relativistic quark potential model is used to describe the quark-antiquark system. The complex-mass formula is obtained from two exact asymptotic solutions for the QCD motivated…
The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is…
We provide optimized recursion relations for homodyne tomography. We improve previous methods by mitigating the divergences intrinsic in the calculation of the pattern functions used previously, and detail how to implement the data analysis…
The structured low-rank approximation problem for general affine structures, weighted 2-norms and fixed elements is considered. The variable projection principle is used to reduce the dimensionality of the optimization problem. Algorithms…
A new computational method for reconstructing a potential from the Dirichlet-to-Neumann map at positive energy is developed. The method is based on D-bar techniques and it works in absence of exceptional points -- in particular, if the…
We prove the Plancherel formula for hypergeometric functions associated to a root system in the situation when the root multiplicities are negative (but close to 0). As a result we obtain a classification of the hypergeometric functions…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
By using the \emph{Rydberg--Klein--Rees} (RKR) formulas to solve the inverse Schr\"{o}dinger problem, we found a confining bottom-up potential from a given eigenvalue spectrum. To illustrate this methodology, we consider the vector meson…
In the present paper we study the structure of the WKB series for the polynomial potential $V(x)=x^N$ ($N$ even). In particular, we obtain relatively simple recurrence formula of the coefficients $\s'_k$ of the semiclassical approximation…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…