Related papers: A nested divide-and-conquer method for tensor Sylv…

The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…

Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified…

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…

In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…

For solving the continuous Sylvester equation, a class of the multiplicative splitting iteration method is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations…

In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…

We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…

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…

In this paper we explore a numerical scheme for a nonlinear fourth order system of partial differential algebraic equations that describes the dynamics of slender inextensible elastica as they arise in the technical textile industry.…

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of…

This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…

Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…

We propose a divide-and-conquer approach to filtering which decomposes the state variable into low-dimensional components to which standard particle filtering tools can be successfully applied and recursively merges them to recover the full…

The numerical solution of algebraic tensor equations is a largely open and challenging task. Assuming that the operator is symmetric and positive definite, we propose two new gradient-descent type methods for tensor equations that…

In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…

Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density…

We study how the divide and conquer principle --- partition the available data into subsamples, compute an estimate from each subsample and combine these appropriately to form the final estimator --- works in non-standard problems where…