相关论文: Absolute value preconditioning for symmetric indef…

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…

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…

We introduce a perturbed preconditioned gradient descent (PPGD) method for the unconstrained minimization of a strongly convex objective $G$ with a locally Lipschitz continuous gradient. We assume that $G(v)=E(v)+F(v)$ and that the gradient…

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

In this article we construct and analyze multigrid preconditioners for discretizations of operators of the form D+K* K, where D is the multiplication with a relatively smooth positive function and K is a compact linear operator. These…

Widely employed for the accurate solution of the electroencephalography forward problem, the symmetric formulation gives rise to a first kind, ill-conditioned operator ill-suited for complex modelling scenarios. This work presents a novel…

We study deterministic matrix completion problem, i.e., recovering a low-rank matrix from a few observed entries where the sampling set is chosen as the edge set of a Ramanujan graph. We first investigate projected gradient descent (PGD)…

In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of ${\cal O}(N)$ elements, we present a construction of an auxiliary coarse grid hierarchy on which a geometric…

Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…

Uniform preconditioners for operators of negative order discretized by (dis)continuous piecewise polynomials of any order are constructed from a boundedly invertible operator of opposite order discretized by continuous piecewise linears.…

Coupled multiphysics problems often give rise to interface conditions naturally formulated in fractional Sobolev spaces. Here, both positive and negative fractionality are common. When designing efficient solvers for discretizations of such…

A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite…

Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…

Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by…

We consider parameterized variational inverse problems that are constrained by partial differential equations (PDEs). We seek to efficiently compute the solution of the inverse problem when auxiliary model parameters, which appear in the…

Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model…

Given a multigrid procedure for linear systems with coefficient matrices $A_n$, we discuss the optimality of a related multigrid procedure with the same smoother and the same projector, when applied to properly related algebraic problems…

Uni- and bivariate data smoothing with spline functions is a well established method in nonparametric regression analysis. The extension to multivariate data is straightforward, but suffers from exponentially increasing memory and…

Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…

We show that the mass matrix derived from finite elements can be effectively used as a preconditioner for iteratively solving the linear system arising from finite-difference discretization of the Poisson equation, using the conjugate…