Related papers: Parallel Gauss-Jordan Elimination and System Reduc…
A constructive approach to get the reduced row echelon form of a given matrix $A$ is presented. It has been shown that after the $k$th step of the Gauss-Jordan procedure, each entry $a^k_{ij}(i<>j; j > k)$ in the new matrix $A^k$ can always…
In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows…
Large-scale linear complementarity problems (LCPs) are repeatedly solved in interactive rigid-body simulations. The projected Gauss-Seidel method is often employed for LCPs, since it has advantages in computation time, numerical robustness,…
Grover's algorithm is a cornerstone of quantum search algorithm, offering quadratic speedup for unstructured problems. However, limited qubit counts and noise in today's noisy intermediate-scale quantum (NISQ) devices hinder large-scale…
This article presents a compact implementation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan…
We apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To resolve the fast-switching excitations, small time steps are…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The…
As a competitive recovery method for heavy oil, In-Situ Combustion (ISC) shows its great potential accompanied by technological advances in recent years. Reservoir simulation will play an indispensable role in the prediction of the…
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…
Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, as well as quantum tunneling phenomena. The most common theoretical…
Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…
In this paper, we study the MapReduce framework from an algorithmic standpoint and demonstrate the usefulness of our approach by designing and analyzing efficient MapReduce algorithms for fundamental sorting, searching, and simulation…
Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…
This paper proposes a receding horizon active learning and control problem for dynamical systems in which Gaussian Processes (GPs) are utilized to model the system dynamics. The active learning objective in the optimization problem is…
In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…