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Gaussian processes are widely used in machine learning domains but remain computationally demanding, limiting their efficient scalability across emerging hardware platforms. The GPRat library addresses these challenges using the HPX…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
Traditional low-rank approximation is a powerful tool to compress the huge data matrices that arise in simulations of partial differential equations (PDE), but suffers from high computational cost and requires several passes over the PDE…
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
In this paper, we describe the performance of an $N$-body simulation of star cluster with 64k stars on a Cray XD1 system with 400 dual-core Opteron processors. A number of astrophysical $N$-body simulations were reported in SCxy…
Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…
General Matrix Multiplication (GEMM) is a fundamental operation widely used in scientific computations. Its performance and accuracy significantly impact the performance and accuracy of applications that depend on it. One such application…
There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even…
In this paper, we describe the implementation and performance of GreeM, a massively parallel TreePM code for large-scale cosmological N-body simulations. GreeM uses a recursive multi-section algorithm for domain decomposition. The size of…
Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…
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 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…
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…
Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
The interpolative decomposition (ID) aims to construct a low-rank approximation formed by a basis consisting of row/column skeletons in the original matrix and a corresponding interpolation matrix. This work explores fast and accurate ID…