Related papers: Multidimensional moment problem and diagonal Schur…
The moment problem is an important problem in Functional Analysis and in Probability measure. It goes back to Stieltjes, around 1890. There is still an important ongoing interest in the recent literature. But, up today, the main theoretical…
Recently, a novel bifurcation technique known as the deflated continuation method (DCM) was applied to the single-component nonlinear Schr\"odinger (NLS) equation with a parabolic trap in two spatial dimensions. The bifurcation analysis…
In this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrodinger equations in a multidimensional case, which tells that not all the solutions are Bloch…
A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
The notion of moment differentiation is extended to the set of generalized multisums of formal power series via an appropriate integral representation and accurate estimates of the moment derivatives. The main result is applied to…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
The $d$-dimensional pattern matching problem is to find an occurrence of a pattern of length $m \times \dots \times m$ within a text of length $n \times \dots \times n$, with $n \ge m$. This task models various problems in text and image…
In this paper, the connections are investigated between two different approaches towards the parametrization of multivariable stable all-pass systems in discrete-time. The first approach involves the tangential Schur algorithm, which…
In the following paper, we present a consistent Newton-Schur solution approach for variational multiscale formulations of the time-dependent Navier-Stokes equations in three dimensions. The main contributions of this work are a systematic…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum entropy…
The generalized problem of moments is a conic linear optimization problem over the convex cone of positive Borel measures with given support. It has a large variety of applications, including global optimization of polynomials and rational…
In this paper we study the truncated operator trigonometric moment problem. All solutions of the moment problem are described by a Nevanlinna-type parameterization. In the case of moments acting in a separable Hilbert space, the matrices of…
Three pseudospectral algorithms are described (Euler, leapfrog and trapez) for solving numerically the time dependent nonlinear Schroedinger equation in one, two or three dimensions. Numerical stability regions in the parameter space are…
Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
This paper is about the moment problem on a finite-dimensional vector space of continuous functions. We investigate the structure of the convex cone of moment functionals (supporting hyperplanes, exposed faces, inner points) and treat…
For the two-dimensional Schr\"odinger equation, the general form of the point transformations such that the result can be interpreted as a Schr\"odinger equation with effective (i.e. position dependent) mass is studied. A wide class of such…
Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…