Related papers: Uniform preconditioners of linear complexity for p…
We consider an automatic construction of locally optimal preconditioners for positive definite linear systems. To achieve this goal, we introduce a differentiable loss function that does not explicitly include the estimation of minimal…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
In this study, we consider a class of linear matroid interdiction problems, where the feasible sets for the upper-level decision-maker (referred to as a leader) and the lower-level decision-maker (referred to as a follower) are induced by…
We study optimal diagonal preconditioning using the classical worst-case $\kappa$-condition number and the averaging-based $\omega$-condition number. For the $\kappa$-optimal preconditioning problem, we derive an affine-based pseudoconvex…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
The multilevel Schwarz preconditioner is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its parallel implementation on arbitrary unstructured triangular/tetrahedral…
We show that a combination of two simple preprocessing steps would generally improve the conditioning of a homogeneous system of linear inequalities. Our approach is based on a comparison among three different but related notions of…
In the past decade, there are many works on the finite element methods for the fully nonlinear Hamilton--Jacobi--Bellman (HJB) equations with Cordes condition. The linearised systems have large condition numbers, which depend not only on…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
In this paper, we describe families of those bounded linear operators on a separable Hilbert space that are simultaneously unitarily equivalent to integral operators on $L_2(R)$ with bounded and arbitrarily smooth Carleman kernels. The main…
We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic…
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to…
A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient…
PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically…
In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the…
A linear constraint system is specified by linear equations over the group $\ZZ_d$ of integers modulo $d$. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the…
In this paper, we investigate the preconditioned AOR method for solving linear systems. We study two general preconditioners and propose some lower triangular, upper triangular and combination preconditioners. For $A$ being an L-matrix, a…