Related papers: Generalized Filtering Decomposition
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…
Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…
In this paper we present general-purpose preconditioners for regularized augmented systems arising from optimization problems, and their corresponding normal equations. We discuss positive definite preconditioners, suitable for CG and…
In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equivalence and additive Schwarz methods. The high-order…
Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…
The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan [15,17] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has…
We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…
In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…
The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…
This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…
Polynomial preconditioning is an important tool in solving large linear systems and eigenvalue problems. A polynomial from GMRES can be used to precondition restarted GMRES and restarted Arnoldi. Here we give methods for indefinite matrices…
We propose a generalized CUR (GCUR) decomposition for matrix pairs $(A, B)$. Given matrices $A$ and $B$ with the same number of columns, such a decomposition provides low-rank approximations of both matrices simultaneously, in terms of some…
Sparse matrix reordering can significantly reduce the fill-in during matrix factorization, thereby decreasing the computational and storage requirements in sparse matrix computations. Finding a minimal fill-in ordering is known to be an…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…
This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of…
We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a…
This is the first of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The non-zero entries in the output are chosen to…
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…