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Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
In this paper, we investigate a class of non-convex sum-of-ratios programs relevant to decision-making in key areas such as product assortment and pricing, and facility location and cost planning. These optimization problems, characterized…
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…
One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of…
The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…
For real matrices of full column-rank, we analyze the conditioning of several types of normal equations that are preconditioned by a randomized preconditioner computed in lower precision. These include symmetrically preconditioned normal…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
In this paper, we investigate the butterfly factorization problem, i.e., the problem of approximating a matrix by a product of sparse and structured factors. We propose a new formal mathematical description of such factors, that encompasses…
Preconditioning is a key component of MCMC algorithms that improves sampling efficiency by facilitating exploration of geometrically complex target distributions through an invertible map. While linear preconditioners are often sufficient…
Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional…
In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
In inverting large sparse matrices, the key difficulty lies in effectively exploiting sparsity during the inversion process. One well-established strategy is the nested dissection, which seeks the so-called sparse Cholesky factorization. We…
This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence…
Solving systems of linear equations is a problem occuring frequently in water engineering applications. Usually the size of the problem is too large to be solved via direct factorization. One can resort to iterative approaches, in…