Related papers: parGeMSLR: A Parallel Multilevel Schur Complement …
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
We evaluate optimized parallel sparse matrix-vector operations for two representative application areas on widespread multicore-based cluster configurations. First the single-socket baseline performance is analyzed and modeled with respect…
We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…
Applying machine learning techniques to the quickly growing data in science and industry requires highly-scalable algorithms. Large datasets are most commonly processed "data parallel" distributed across many nodes. Each node's contribution…
We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…
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…
Preconditioning for overdetermined least-squares problems has received comparatively little attention, and designing methods that are both effective and memory-efficient remains challenging. We propose a class of ILU-based preconditioners…
High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em…
Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…
Sparse matrix-vector multiplication (SpMV) is a fundamental operation in machine learning, scientific computing, and graph algorithms. In this paper, we investigate the space, time, and energy efficiency of SpMV using various compressed…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
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…
The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…
Sparse data structures are commonly used in neural networks to reduce the memory footprint. These data structures are compact but cause irregularities such as random memory accesses, which prevent efficient use of the memory hierarchy. GPUs…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
This work introduces TapirXLA, a replacement for TensorFlow's XLA compiler that embeds recursive fork-join parallelism into XLA's low-level representation of code. Machine-learning applications rely on efficient parallel processing to…
We propose a new sparse matrix format, PackSELL, designed to support diverse data representations and enable efficient sparse matrix-vector multiplication (SpMV) on GPUs. Building on sliced ELLPACK (SELL), PackSELL incorporates delta…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…
A new format for storing sparse matrices is proposed for efficient sparse matrix-vector (SpMV) product calculation on modern graphics processing units (GPUs). This format extends the standard compressed row storage (CRS) format and can be…