Search Results - "Triangular solves"

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…”
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Developing a Multi-GPU-Enabled Preconditioned GMRES with Inexact Triangular Solves for Block Sparse Matrices by Ma, Wenpeng, Hu, Yiwen, Yuan, Wu, Liu, Xiazhen

“… In this paper, we propose and implement an iterative, inexact block triangular solve on multi-GPUs based on PETSc’s framework…”
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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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Hypergraph Partitioning and Reordering for Parallel Sparse Triangular Solves and Tensor Decomposition by Torun, Tuğba

“…Several scientific and real-world problems require computations with sparse ma-trices, or more generally, sparse tensors which are multi-dimensional arrays. For…”
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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 preconditioner…”
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Multicore Performance Engineering of Sparse Triangular Solves Using a Modified Roofline Model by Wittmann, Markus, Hager, Georg, Janalik, Radim, Lanser, Martin, Klawonn, Axel, Rheinbach, Oliver, Schenk, Olaf, Wellein, Gerhard

“… The model can thus provide an insightful visualization of bottlenecks. In this paper, we try to establish realistic bandwidth ceilings for the sparse triangular solve…”
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Accelerating eigenvector and pseudospectra computation using blocked multi-shift triangular solves by Moon, Tim, Poulson, Jack

“…Multi-shift triangular solves are basic linear algebra calculations with applications in eigenvector and pseudospectra computation…”
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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

“… In this paper, we investigate the performance of the BLR triangular solve phase, which we observe to be underwhelming when dealing with many right-hand sides (RHS…”
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YuenyeungSpTRSV: A Thread-Level and Warp-Level Fusion Synchronization-Free Sparse Triangular Solve by Zhang, Feng, Su, Jiya, Liu, Weifeng, He, Bingsheng, Wu, Ruofan, Du, Xiaoyong, Wang, Rujia

“…Sparse triangular solves (SpTRSVs) are widely used in linear algebra domains, and several GPU-based SpTRSV algorithms have been developed…”
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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…”
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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…”
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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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Scaled ILU smoothers for Navier–Stokes pressure projection by Thomas, Stephen, Carr, Arielle, Mullowney, Paul, Świrydowicz, Katarzyna, Day, Marcus

“…‐frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs…”
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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, where dataflows can be categorized into coarse and fine granularity…”
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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…”
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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

“… multiplication and sparse triangular solves with minimal overheads. The framework achieves these goals by using a collection of traditional permutations, point-to-point…”
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Locality Aware Reordering for Sparse Triangular Solve by Torun, Tuğba

“…Sparse Triangular Solve (SpTS) is a commonly used kernel in a wide variety of scientific and engineering applications…”
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