Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers
Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers
复制标题
DOI：
10.1002/cpe.4460
复制
发表时间：
2019-03-25
影响因子：
2
通讯作者：
Quintana-Orti, Enrique S.
中科院分区：
文献类型：
--
作者：
Anzt, Hartwig;Dongarra, Jack;Quintana-Orti, Enrique S.
我们提出了一种自适应方案，通过以不同精度格式（半精度、单精度或双精度）选择性地存储块雅可比预处理器的对角块来减少数据移动引起的通信开销。然后，这种专门的预处理器可以与任何 Krylov 子空间方法相结合，用于求解稀疏线性系统，以双精度执行所有算术。我们评估自适应精度预处理器对预处理共轭梯度求解器的迭代计数和数据传输成本的影响。一般来说，预条件共轭梯度法是一种内存带宽限制算法，因此其执行时间和能耗很大程度上取决于访问内存中问题数据的成本。鉴于这一观察结果，我们提出了一个模型，该模型可以量化我们的方法所节省的时间和能源，前提是这两种成本线性依赖于浮点数的位长度。此外，我们使用 SuiteSparse 矩阵集合中的许多测试问题来估计自适应块雅可比预处理方案的潜在优势。
We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block-Jacobi preconditioner in different precision formats (half, single, or double). This specialized preconditioner can then be combined with any Krylov subspace method for the solution of sparse linear systems to perform all arithmetic in double precision. We assess the effects of the adaptive precision preconditioner on the iteration count and data transfer cost of a preconditioned conjugate gradient solver. A preconditioned conjugate gradient method is, in general, a memory bandwidth-bound algorithm, and therefore its execution time and energy consumption are largely dominated by the costs of accessing the problem's data in memory. Given this observation, we propose a model that quantifies the time and energy savings of our approach based on the assumption that these two costs depend linearly on the bit length of a floating point number. Furthermore, we use a number of test problems from the SuiteSparse matrix collection to estimate the potential benefits of the adaptive block-Jacobi preconditioning scheme.