Related papers: A parallel structured divide-and-conquer algorithm…

PDDSparse is a new hybrid parallelisation scheme for solving large-scale elliptic boundary value problems on supercomputers, which can be described as a Feynman-Kac formula for domain decomposition. At its core lies a stochastic linear,…

The solution of sparse linear systems constitutes the dominant computational bottleneck in interior point methods (IPMs), frequently consuming over 70% of the total solution time. As optimization problems scale to millions of variables,…

In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid…

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…

In this paper, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and computation cost of the…

In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplication of a matrix with…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…

We provide several algorithms for the exact, uniform random sampling of Latin squares and Sudoku matrices via probabilistic divide-and-conquer (PDC). Our approach divides the sample space into smaller pieces, samples each separately, and…

Pushdown systems (PDSs) and recursive state machines (RSMs), which are linearly equivalent, are standard models for interprocedural analysis. Yet RSMs are more convenient as they (a) explicitly model function calls and returns, and (b)…

We propose a computationally and statistically efficient divide-and-conquer (DAC) algorithm to fit sparse Cox regression to massive datasets where the sample size $n_0$ is exceedingly large and the covariate dimension $p$ is not small but…

In this paper, we introduce a primal-dual algorithmic framework for solving Symmetric Cone Programs (SCPs), a versatile optimization model that unifies and extends Linear, Second-Order Cone (SOCP), and Semidefinite Programming (SDP). Our…

Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…

We present a high-performance solver for dense skew-symmetric matrix eigenvalue problems. Our work is motivated by applications in computational quantum physics, where one solution approach to solve the so-called Bethe-Salpeter equation…

We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or…