Silent Data Corruption Resilient Two-sided Matrix Factorizations
Silent Data Corruption Resilient Two-sided Matrix Factorizations
复制标题
静默数据损坏弹性双边矩阵分解
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Zizhong Chen
中科院分区：
文献类型：
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作者：
Panruo Wu;Nathan Debardeleben;Qiang Guan;S. Blanchard;Jieyang Chen;Dingwen Tao;Xin Liang;Kaiming Ouyang;Zizhong Chen
本文提出了一种基于算法的容错方法来加固三个双边矩阵分解的软错误：减少到Hessenberg形式，三对角形式，和双对角形式。这些双边分解通常是计算特征值/特征向量和奇异值分解的先决条件。基于容错的算法已被证明对三种主要的单侧矩阵分解有效：LU，Cholesky和QR，但将其扩展到覆盖双侧分解是不平凡的，因为没有明显的 extit{offline，problem}特定的校验和维护。因此，我们开发了一个 extit{online，algorithm}特定的校验和方案，并展示如何系统地适应LAPACK和ScaLAPACK包中使用的双侧因子分解算法，以引入基于容错的算法。由此产生的ABFT方案可以检测和纠正算术错误 在允许及时错误处理的因式分解过程中{连续} extit。详细的分析和实验表明，成本和收益的弹性。我们证明，我们的计划涵盖了很大一部分的操作的因式分解。我们的校验和方案实现了高的错误检测覆盖率和错误纠正覆盖率相比，最先进的，具有低开销和高可扩展性。
This paper presents an algorithm based fault tolerance method to harden three two-sided matrix factorizations against soft errors: reduction to Hessenberg form, tridiagonal form, and bidiagonal form. These two sided factorizations are usually the prerequisites to computing eigenvalues/eigenvectors and singular value decomposition. Algorithm based fault tolerance has been shown to work on three main one-sided matrix factorizations: LU, Cholesky, and QR, but extending it to cover two sided factorizations is non-trivial because there are no obvious extit{offline, problem} specific maintenance of checksums. We thus develop an extit{online, algorithm} specific checksum scheme and show how to systematically adapt the two sided factorization algorithms used in LAPACK and ScaLAPACK packages to introduce the algorithm based fault tolerance. The resulting ABFT scheme can detect and correct arithmetic errors extit{continuously} during the factorizations that allow timely error handling. Detailed analysis and experiments are conducted to show the cost and the gain in resilience. We demonstrate that our scheme covers a significant portion of the operations of the factorizations. Our checksum scheme achieves high error detection coverage and error correction coverage compared to the state of the art, with low overhead and high scalability.