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Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…
In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the…
Alternating minimization heuristics seek to solve a (difficult) global optimization task through iteratively solving a sequence of (much easier) local optimization tasks on different parts (or blocks) of the input parameters. While popular…
In this study, a new $\Delta$-evaluation method is introduced for solving a column permutation problem defined on a sparse binary matrix with the consecutive ones property. This problem models various $\mathcal{NP}$-hard problems in graph…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…
Alternating Direction Method of Multipliers (ADMM) algorithm has been widely adopted for solving the distributed optimization problem (DOP). In this paper, a new distributed parallel ADMM algorithm is proposed, which allows the agents to…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
A major impediment towards the industrial adoption of decentralized distributed systems comes from the difficulty to theoretically prove that these systems exhibit the required behavior. In this paper, we use probability theory to analyze a…
A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…
Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…
It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating…
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…
Recently, some mixture algorithms of pointwise and pairwise learning (PPL) have been formulated by employing the hybrid error metric of "pointwise loss + pairwise loss" and have shown empirical effectiveness on feature selection, ranking…
Nowadays, more and more datasets are stored in a distributed way for the sake of memory storage or data privacy. The generalized eigenvalue problem (GEP) plays a vital role in a large family of high-dimensional statistical models. However,…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive…
We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the…
The Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method is a cutting-edge distributed optimization algorithm known for its superior numerical performance. It relies on each agent transmitting information to a central…