Related papers: A Matrix Approach to Numerical Solution of the DGL…
We present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming approach and another convex minimization method supported…
A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a…
We consider a hierarchy of the natural type Hamiltonian systems of $n$ degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of $2\times 2$…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…
In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac-Frenkel…
The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It…
Unsupervised integrative analysis of multiple data sources has become common place and scalable algorithms are necessary to accommodate ever increasing availability of data. Only few currently methods have estimation speed as their focus,…
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…
This paper presents a solution to the nonlinear small x ``projectile side'' evolution equations as derived by Balitskii in 1996. The solution is based on functional Fokker-Planck methods. The fixed point at small x is explicitly calculated…
Although Galerkin discretizations have been intensively employed in the IgA context, an efficient implementation requires special numerical quadrature rules when constructing the system of equations. To avoid this issue, isogeometric…
We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical…
In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
It is quite common that a nonlinear partial differential equation (PDE) admits multiple distinct solutions and each solution may carry a unique physical meaning. One typical approach for finding multiple solutions is to use the Newton…
The traditional method of factorization can be used to obtain only the particular solutions of the Li\'enard type ordinary differential equations. We suggest a modification of the approach that can be used to construct general solutions .…
We propose a numerical method to spline-interpolate discrete signals and then apply the integral transforms to the corresponding analytical spline functions. This represents a robust and computationally efficient technique for estimating…
While mixed-integer linear programming and convex programming solvers have advanced significantly over the past several decades, solution technologies for general mixed-integer nonlinear programs (MINLPs) have yet to reach the same level of…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
The numerical solution of parameter identification inverse problems for kinetic equations can exhibit high computational and memory costs. In this paper, we propose a dynamical low-rank scheme for the reconstruction of the scattering…