Related papers: Linear Complexity $\mathcal{H}^2$ Direct Solver fo…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
This paper introduces hybrid LU-QR al- gorithms for solving dense linear systems of the form Ax = b. Throughout a matrix factorization, these al- gorithms dynamically alternate LU with local pivoting and QR elimination steps, based upon…
Parallel computing is very important to accelerate the performance of software systems. Additionally, considering that a recurring challenge is to process high data volumes continuously, stream processing emerged as a paradigm and software…
As the artificial intelligence community advances into the era of large models with billions of parameters, distributed training and inference have become essential. While various parallelism strategies-data, model, sequence, and…
Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser-matter interactions with Particle-In-Cell (PIC)…
The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct…
Large-scale, parallel clusters composed of commodity processors are increasingly available, enabling the use of vast processing capabilities and distributed RAM to solve hard search problems. We investigate Hash-Distributed A* (HDA*), a…
Scheduling query execution plans is a particularly complex problem in shared-nothing parallel systems, where each site consists of a collection of local time-shared (e.g., CPU(s) or disk(s)) and space-shared (e.g., memory) resources and…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
We present a parallel algorithm for computing the approximate factorization of an $N$-by-$N$ kernel matrix. Once this factorization has been constructed (with $N \log^2 N $ work), we can solve linear systems with this matrix with $N \log N…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…
Deploying mixed-precision neural networks on edge devices is friendly to hardware resources and power consumption. To support fully mixed-precision neural network inference, it is necessary to design flexible hardware accelerators for…
Pattern matching of streaming time series with lower latency under limited computing resource comes to a critical problem, especially as the growth of Industry 4.0 and Industry Internet of Things. However, against traditional single pattern…
In this paper we analyze, evaluate, and improve the performance of training generalized linear models on modern CPUs. We start with a state-of-the-art asynchronous parallel training algorithm, identify system-level performance bottlenecks,…
Data processing systems offer an ever increasing degree of parallelism on the levels of cores, CPUs, and processing nodes. Query optimization must exploit high degrees of parallelism in order not to gradually become the bottleneck of query…
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
Hierarchical $\mathcal{H}^2$-matrices are asymptotically optimal representations for the discretizations of non-local operators such as those arising in integral equations or from kernel functions. Their $O(N)$ complexity in both memory and…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…