Search Results - "Triangular solves"

Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning by Chow, Edmond, Anzt, Hartwig, Scott, Jennifer, Dongarra, Jack

“…When using incomplete factorization preconditioners with an iterative method to solve large sparse linear systems, each application of the preconditioner…”
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Incomplete Sparse Approximate Inverses for Parallel Preconditioning by Anzt, Hartwig, Huckle, Thomas K., Bräckle, Jürgen, Dongarra, Jack

“…•A new preconditioning technique based on combining incomplete factorizations with Frobenius norm minimization. We call this preconditioner “Incomplete Sparse…”
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GraphOpt: Constrained-Optimization-Based Parallelization of Irregular Graphs by Shah, Nimish, Meert, Wannes, Verhelst, Marian

“…Sparse, irregular graphs show up in various applications like linear algebra, machine learning, engineering simulations, robotic control, etc. These graphs…”
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Incomplete Sparse Approximate Inverses for Parallel Preconditioning by Anzt, Hartwig, Huckle, Thomas K., Bräckle, Jürgen, Dongarra, Jack

“…In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse…”
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A Comparative Study of Block Incomplete Sparse Approximate Inverses Preconditioning on Tesla K20 and V100 GPUs by Ma, Wenpeng, Yuan, Wu, Liu, Xiazhen

“…Incomplete Sparse Approximate Inverses (ISAI) has shown some advantages over sparse triangular solves on GPUs when it is used for the incomplete LU based…”
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Fast synchronization‐free algorithms for parallel sparse triangular solves with multiple right‐hand sides by Liu, Weifeng, Li, Ang, Hogg, Jonathan D., Duff, Iain S., Vinter, Brian

“…Summary The sparse triangular solve kernels, SpTRSV and SpTRSM, are important building blocks for a number of numerical linear algebra routines. Parallelizing…”
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Efficient Hardware Accelerator Based on Medium Granularity Dataflow for SpTRSV by Chen, Qian, Yang, Xiaofeng, Lu, Shengli

“…Sparse triangular solve (SpTRSV) is widely used in various domains. Numerous studies have been conducted using CPUs, GPUs, and specific hardware accelerators,…”
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Communication Avoiding Block Low-Rank Parallel Multifrontal Triangular Solve with Many Right-Hand Sides by Amestoy, Patrick, Boiteau, Olivier, Buttari, Alfredo, Gerest, Matthieu, Jézéquel, Fabienne, L’Excellent, Jean-Yves, Mary, Theo

“…Block low-rank (BLR) compression can significantly reduce the memory and time costs of parallel sparse direct solvers. In this paper, we investigate the…”
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A Split Execution Model for SpTRSV by Ahmad, Najeeb, Yilmaz, Buse, Unat, Didem

“…Sparse Triangular Solve (SpTRSV) is an important and extensively used kernel in scientific computing. Parallelism within SpTRSV depends upon matrix sparsity…”
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An on-node scalable sparse incomplete LU factorization for a many-core iterative solver with Javelin by Booth, Joshua Dennis, Bolet, Gregory

“…We present a scalable incomplete LU factorization to be used as a preconditioner for solving sparse linear systems with iterative methods in the package called…”
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TileSpTRSV: a tiled algorithm for parallel sparse triangular solve on GPUs by Lu, Zhengyang, Liu, Weifeng

“…Sparse triangular solve (SpTRSV) is one of the most important level-2 kernels in sparse basic linear algebra subprograms (BLAS). Compared to another level-2…”
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DPU-v2: Energy-efficient execution of irregular directed acyclic graphs by Shah, Nimish, Meert, Wannes, Verhelst, Marian

“…A growing number of applications like probabilistic machine learning, sparse linear algebra, robotic navigation, etc., exhibit irregular data flow computation…”
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A parallel sparse triangular solve algorithm based on dependency elimination of the solution vector by Jin, Song, Pei, Songwei, Wang, Yu, Qi, Yincheng

“…Sparse triangular solve (SpTRSV) is an important kernel in many scientific computing applications. In traditional viewpoints, accelerating SpTRSV by…”
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A Fast Dense Triangular Solve in CUDA by Hogg, J. D.

“…The level 2 BLAS operation _trsv performs a dense triangular solve and is often used in the solve phase of a direct solver following a matrix factorization…”
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Unified Communication Optimization Strategies for Sparse Triangular Solver on CPU and GPU Clusters by Liu, Yang, Ding, Nan, Sao, Piyush, Williams, Samuel, Li, Xiaoye Sherry

“…This paper presents a unified communication optimization frame-work for sparse triangular solve (SpTRSV) algorithms on CPU and GPU clusters. The framework…”
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