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We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified…
Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In…
We develop a fast solver for the spectral element method (SEM) applied to the two-sided fractional diffusion equation on uniform, geometric and graded meshes. By approximating the singular kernel with a degenerate kernel, we construct a…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…
We present a randomized algorithm that, on input a symmetric, weakly diagonally dominant n-by-n matrix A with m nonzero entries and an n-vector b, produces a y such that $\norm{y - \pinv{A} b}_{A} \leq \epsilon \norm{\pinv{A} b}_{A}$ in…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport…
In this paper, we present new stochastic methods for solving two important classes of nonconvex optimization problems. We first introduce a randomized accelerated proximal gradient (RapGrad) method for solving a class of nonconvex…
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…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
This paper presents two novel algorithms for approximately projecting symmetric matrices onto the Positive Semidefinite (PSD) cone using Randomized Numerical Linear Algebra (RNLA). Classical PSD projection methods rely on full-rank…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between…