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It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision…

The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is…

The efficient generation of meshes is an important step in the numerical solution of various problems in physics and engineering. We are interested in situations where global mesh quality and tight coupling to the physical solution is…

Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…

This paper studies a class of distributed optimization algorithms by a set of agents, where each agent has only access to its own local convex objective function, and jointly minimizes the sum of the functions. The communications among…

Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…

Semi-parallel, or folded, VLSI architectures are used whenever hardware resources need to be saved at design time. Most recent applications that are based on Projective Geometry (PG) based balanced bipartite graph also fall in this…

Sparse linear algebra routines are fundamental building blocks of a large variety of scientific applications. Direct solvers, which are methods for solving linear systems via the factorization of matrices into products of triangular…

Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…

We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the…

We introduce the sparsified Cholesky and sparsified multigrid algorithms for solving systems of linear equations. These algorithms accelerate Gaussian elimination by sparsifying the nonzero matrix entries created by the elimination process.…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…

Positive linear programs (LPs) model many graph and operations research problems. One can solve for a $(1+\epsilon)$-approximation for positive LPs, for any selected $\epsilon$, in polylogarithmic depth and near-linear work via variations…

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex…

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block…

We present a distributed parallel mesh curving method for virtual geometry. The main application is to generate large-scale curved meshes on complex geometry suitable for analysis with unstructured high-order methods. Accordingly, we devise…

While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…