Related papers: RCHOL: Randomized Cholesky Factorization for Solvi…

This paper is about randomized iterative algorithms for solving a linear system of equations $X \beta = y$ in different settings. Recent interest in the topic was reignited when Strohmer and Vershynin (2009) proved the linear convergence…

The dominant cost in solving least-square problems using Newton's method is often that of factorizing the Hessian matrix over multiple values of the regularization parameter ($\lambda$). We propose an efficient way to interpolate the…

This work is about rounding error analysis of randomized CholeskyQR-type algorithms for sparse matrices. We often encounter QR factorization of the sparse matrices in many real problems. In this work, we focus on some typical…

Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…

In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization…

Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…

Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce high-quality Markov chain Monte Carlo-output even for very challenging target distributions. To this end, a symmetric positive definite scaling matrix for RMHMC,…

We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their…

We introduce a geometric stencil selection algorithm for Laplacian in 3D that significantly improves octant-based selection considered earlier. The goal of the algorithm is to choose a small subset from a set of irregular points surrounding…

In the topological study of distributed systems, the immediate snapshot is the fundamental computation block for the topological characterization of wait-free solvable tasks. However, in reality, the immediate snapshot is not available as a…

Web-based interactions can be frequently represented by an attributed graph, and node clustering in such graphs has received much attention lately. Multiple efforts have successfully applied Graph Convolutional Networks (GCN), though with…

Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…

In this article, we present the first deterministic directed Laplacian L systems solver that runs in time almost-linear in the number of non-zero entries of L. Previous reductions imply the first deterministic almost-linear time algorithms…

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…

Column generation (CG) is a vital method to solve large-scale problems by dynamically generating variables. It has extensive applications in common combinatorial optimization, such as vehicle routing and scheduling problems, where each…

While existing algorithms may be used to solve a linear system over a general field in matrix-multiplication time, the complexity of constructing a symmetric triangular factorization (LDL) has received relatively little formal study. The…

Cholesky linear solvers are a critical bottleneck in challenging applications within computer graphics and scientific computing. These applications include but are not limited to elastodynamic barrier methods such as Incremental Potential…

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…

Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large…