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Comparative Study of Mixed-Precision and Low-Rank Compression Techniques in Sparse Direct Solvers

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Titel: Comparative Study of Mixed-Precision and Low-Rank Compression Techniques in Sparse Direct Solvers
Autoren: Nicolas, Brieuc, Faverge, Mathieu, Ramet, Pierre, Lisito, Alycia, Kherraz, Mohamed
Weitere Verfasser: Nicolas, Brieuc
Verlagsinformationen: 2024.
Publikationsjahr: 2024
Schlagwörter: Iterative Refinement, LU Factorization, Mixed Precision, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Sparse Direct Solver, Cholesky Factorization, Low Rank Compression
Beschreibung: Sparse direct solvers play a crucial role in numerical simulation and are one of the most time-consuming steps in many applications. Recently, many efforts have been made to reduce the complexity of dense and sparse direct solvers by introducing low-rank compression techniques. These techniques allow applications to reduce the amount of information stored in the matrix, depending on the quality of the solution being sought, and greatly reduce both memory requirements and computational complexity. Another solution driven by the computational capabilities of the hardware is the use of mixed-precision computations. This has been continuously in vogue with new generations of hardware providing single to double performance ratios of more than two. In our study, we extend the sparse direct solver PaStiX to use reduced-precision factorization and compare it to its low-rank strategy in terms of time to solution, numerical stability, memory consumption, and energy consumption. The goal of this study is to evaluate whether the tradeoff between computational speed and solution accuracy is worthwhile, and if so, which strategy, low-rank or mixed-precision, is better.
Publikationsart: Conference object
Sprache: English
Zugangs-URL: https://hal.science/hal-04585047v1
Rights: CC BY
Dokumentencode: edsair.dedup.wf.002..4e5af24f908db38982429468ac9691f3
Datenbank: OpenAIRE
Beschreibung
Abstract:Sparse direct solvers play a crucial role in numerical simulation and are one of the most time-consuming steps in many applications. Recently, many efforts have been made to reduce the complexity of dense and sparse direct solvers by introducing low-rank compression techniques. These techniques allow applications to reduce the amount of information stored in the matrix, depending on the quality of the solution being sought, and greatly reduce both memory requirements and computational complexity. Another solution driven by the computational capabilities of the hardware is the use of mixed-precision computations. This has been continuously in vogue with new generations of hardware providing single to double performance ratios of more than two. In our study, we extend the sparse direct solver PaStiX to use reduced-precision factorization and compare it to its low-rank strategy in terms of time to solution, numerical stability, memory consumption, and energy consumption. The goal of this study is to evaluate whether the tradeoff between computational speed and solution accuracy is worthwhile, and if so, which strategy, low-rank or mixed-precision, is better.