Related papers: An efficient multi-core implementation of a novel …

A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…

Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety…

We design and develop a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication (SpMSpV) where the matrix, the input vector, and the output vector are all sparse. SpMSpV is an important primitive in the…

The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…

Tomographic imaging has benefited from advances in X-ray sources, detectors and optics to enable novel observations in science, engineering and medicine. These advances have come with a dramatic increase of input data in the form of faster…

Sparse matrices and linear algebra are at the heart of scientific simulations. More than 70 sparse matrix storage formats have been developed over the years, targeting a wide range of hardware architectures and matrix types. Each format is…

We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of…

We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…

In this paper we describe HeSP, a complete simulation framework to study a general task scheduling-partitioning problem on heterogeneous architectures, which treats recursive task partitioning and scheduling decisions on equal footing.…

A new generation of manycore processors is on the rise that offers dozens and more cores on a chip and, in a sense, fuses host processor and accelerator. In this paper we target the efficient training of generalized linear models on these…

Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…

We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…

The parallel algorithm for loading large sparse matrices from files into distributed memories of high performance computing (HPC) systems is presented. This algorithm was designed specially for matrices stored in files in the space-effcient…

In this work, we develop a new fast algorithm, spaQR -- sparsified QR, for solving large, sparse linear systems. The key to our approach is using low-rank approximations to sparsify the separators in a Nested Dissection based Householder QR…

Hierarchical low-rank approximation of dense matrices can reduce the complexity of their factorization from O(N^3) to O(N). However, the complex structure of such hierarchical matrices makes them difficult to parallelize. The block size and…

We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to…

We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse…

Modern HPC systems are increasingly relying on greater core counts and wider vector registers. Thus, applications need to be adapted to fully utilize these hardware capabilities. One class of applications that can benefit from this increase…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…