相关论文: Sharpened PCG Iteration Bound for High-Contrast He…

This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…

The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…

We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton…

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…

Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…

Deep learning solvers for partial differential equations typically have limited accuracy. We propose to overcome this problem by using them as preconditioners. More specifically, we apply discretization-invariant neural operators to learn…

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…

This work is on a fast and accurate reduced basis method for solving discretized fractional elliptic partial differential equations (PDEs) of the form $\mathcal{A}^su=f$ by rational approximation. A direct computation of the action of such…

Preconditioned eigenvalue solvers (eigensolvers) are gaining popularity, but their convergence theory remains sparse and complex. We consider the simplest preconditioned eigensolver--the gradient iterative method with a fixed step size--for…

This work studies a composite minimization problem involving a differentiable function q and a nonsmooth function h, both of which may be nonconvex. This problem is ubiquitous in signal processing and machine learning yet remains…

Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…

In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theorybased noniterative or approximate iterative treatments of triple excitations when applied to thedetermination of highly accurate potential energy…

We review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposition method better performance in terms of the number of…

We describe a new approach to derive numerical approximations of boundary conditions for high-order accurate finite-difference approximations. The approach, called the Local Compatibility Boundary Condition (LCBC) method, uses boundary…

We study the high-contrast biharmonic plate equation with HCT and Morley discretizations. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by…

This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…