Stability Analysis of Inline ZFP Compression for Floating-Point Data in Iterative Methods
Stability Analysis of Inline ZFP Compression for Floating-Point Data in Iterative Methods
复制标题
迭代方法中浮点数据内联 ZFP 压缩的稳定性分析
DOI：
10.1137/19m126904
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Peter Lindstrom
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文献类型：
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作者：
Alyson Fox;James Diffenderfer;J. Hittinger;G. Sanders;Peter Lindstrom
目前，许多高性能计算应用中的主要限制是数据容量和带宽，无论是在节点间通信中，还是在节点上的数据移动中都是如此。解决此限制的一种新方法是利用压缩数据数组形式的数据压缩。将数据存储在压缩数据数组中，并在计算期间根据需要转换为标准IEEE-754类型，可以减少带宽和存储的压力。但是，重复转换(有损压缩和解压缩)会引入额外的逼近误差，需要证明这些误差不会显著影响模拟结果。我们将最近的工作[J.Diffenderfer等人，浮点数据的ZFP压缩的误差分析，SIAM科学计算杂志，2019]扩展到时间步进和迭代方案的情况，其中除了转换之外还重复应用推进运算符，其中除了转换之外还重复应用推进运算符。我们证明了包含不动点迭代和时间演化迭代的迭代方法的累积误差在标准约束下是有界的。建立了平稳不动点迭代收敛所需的附加迭代次数的上界。文中还对传统的基于ZFP压缩阵列的平稳迭代算法的前向误差和后向误差进行了分析。给出了几个一维、二维和三维测试问题的结果，以验证理论界限的正确性。
Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both inter-node communications and even more-so in on-node data motion. A new approach to address this limitation is to make use of data compression in the form of a compressed data array. Storing data in a compressed data array and converting to standard IEEE-754 types as needed during a computation can reduce the pressure on bandwidth and storage. However, repeated conversions (lossy compression and decompression) introduce additional approximation errors, which need to be shown to not significantly affect the simulation results. We extend recent work [J. Diffenderfer, et al., Error Analysis of ZFP Compression for Floating-Point Data, SIAM Journal on Scientific Computing, 2019] that analyzed the error of a single use of compression and decompression of the ZFP compressed data array representation [P. Lindstrom, Fixed-rate compressed floating-point arrays, IEEE Transactions on Visualization and Computer Graphics, 2014] to the case of time-stepping and iterative schemes, where an advancement operator is repeatedly applied in addition to the conversions. We show that the accumulated error for iterative methods involving fixed-point and time evolving iterations is bounded under standard constraints. An upper bound is established on the number of additional iterations required for the convergence of stationary fixed-point iterations. An additional analysis of traditional forward and backward error of stationary iterative methods using ZFP compressed arrays is also presented. The results of several 1D, 2D, and 3D test problems are provided to demonstrate the correctness of the theoretical bounds.
影响因子：
2.1
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