Related papers: J-matrix method of scattering for inverse-square s…
We present an iterative algorithm to compute numerical approximations of the potential for the Schr\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle,…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…
For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective…
In this paper, we study the scattering theory for the cubic inhomogeneous Schr\"odinger equations with inverse square potential $iu_t+\Delta u-\frac{a}{|x|^2}u=\lambda |x|^{-b}|u|^2u$ with $a>-\frac14$ and $0<b<1$ in dimension three. In the…
In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…
We prove that the singularities of a potential in the two and three dimensional Schr\"odinger equation are the same as the singularities of the Born approximation (Diffraction Tomography), obtained from backscattering inverse data, with an…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
This article deals with the limiting spectral distribution and joint convergence of reverse circulant and symmetric circulant matrices with independent entries. These results are already proved in articles Bose and Sen (2008)…
We give a brief survey for the recent development of inverse scattering theory on non-compact Riemannian manifolds. The main theme is the reconstruction of the manifold and the metric from the scattering matrix.
We describe inverse scattering for the matrix Schroedinger operator with general selfadjoint boundary conditions at the origin using the Marchenko equation. Our approach allows the recovery of the potential as well as the boundary…
This research focuses on the possibility of the surjective relation between symmetric potential function and its scattering matrix in 1-dimension. The theory bases on the property of wave function symmetry and boundary conditions. This…
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
Nonlinearity arising from mutual interactions is one of the two main difficulties to be addressed in inverse scattering. In this paper, we review and describe under a common rationale some approaches which have been introduced in literature…