Related papers: Symplectic Elimination
Let $A$ be a $n$ by $n$ matrix. A skeleton decomposition is any factorization of the form $CUR$ where $C$ comprises columns of $A$, and $R$ comprises rows of $A$. In this paper, we consider uniformly sampling $\l\simeq k \log n$ rows and…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…
We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
The cyclic reduction (CR) algorithm is an efficient method for solving quadratic matrix equations that arise in quasi-birth-death (QBD) stochastic processes. However, its convergence is not guaranteed when the associated matrix polynomial…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
The Kalman decomposition for Linear Quantum Stochastic Systems in the real quadrature operator representation, that was derived indirectly in [1] by the authors, is derived here directly, using the "one-sided symplectic" SVD-like…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
We consider an $\ell_1$-regularized inverse problem where both the forward and regularization operators have a Kronecker product structure. By leveraging this structure, a joint decomposition can be obtained using generalized singular value…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…
The QR Decomposition (QRD) of communication channel matrices is a fundamental prerequisite to several detection schemes in Multiple-Input Multiple-Output (MIMO) communication systems. Herein, the main feature of the QRD is to transform the…
Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or…
A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. The problem of finding edge-disjoint Hamiltonian cycles in a given regular graph has many applications in combinatorial optimization and…
Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite…
Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially…