Related papers: On efficient block Krylov-solvers for $\mathcal H^…
In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
We introduce a two-level direct solver for the Hierarchical Poincar\'e-Steklov (HPS) method for solving linear elliptic PDEs. HPS combines multidomain spectral collocation with a direct solver, enabling high-order discretizations for highly…
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 introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
A new runtime environment for the execution of recursive matrix algorithms on a supercomputer with distributed memory is proposed. It is designed both for dense and sparse matrices. The environment ensures decentralized control of the…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
The importance of hierarchically structured representations for tractable planning has long been acknowledged. However, the questions of how people discover such abstractions and how to define a set of optimal abstractions remain open. This…
The devices designed for the Internet-of-Things encompass a large variety of distinct processor architectures, forming a highly heterogeneous zoo. In order to tackle this, we employ a simulator to estimate the performance of the…
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…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…
Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…
We develop a novel linear-complexity bottom-up sketching-based algorithm for constructing a $H^2$ matrix, and present its high performance GPU implementation. The construction algorithm requires both a black-box sketching operator and an…
Recent advances in transformer-based foundation models have made them the default choice for many tasks, but their rapidly growing size makes fitting a full model on a single GPU increasingly difficult and their computational cost…
In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…
We consider the problem of developing an efficient multi-threaded implementation of the matrix-vector multiplication algorithm for sparse matrices with structural symmetry. Matrices are stored using the compressed sparse row-column format…
A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in…
Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…
Matrix-free finite element implementations of massively parallel geometric multigrid save memory and are often significantly faster than implementations using classical sparse matrix techniques. They are especially well suited for…