On Improving Linear Solver Performance: A Block Variant of GMRES
On Improving Linear Solver Performance: A Block Variant of GMRES
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DOI：
10.1137/040608088
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发表时间：
2005-11
期刊：
影响因子：
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通讯作者：
A. Baker;J. Dennis;E. Jessup
中科院分区：
文献类型：
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作者：
A. Baker;J. Dennis;E. Jessup
处理器性能和内存访问时间之间不断扩大的差距需要重新检查迭代线性求解器算法中的数据移动。因此，我们探索并建立了以减少数据在内存中移动的方式修改标准迭代线性求解器算法的可行性。特别是，我们提出了重新启动 GMRES 算法的替代方案，用于基于求解块线性系统 $AX=B$ 来求解单个右侧线性系统 $Ax=b$。通过在向量组的运算中使用矩阵 $A$ 可以提高算法性能，即求解时间。实验结果证明了数据移动实现选择的重要性以及新方法对不同应用领域的各种问题的有效性。
The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system $Ax=b$ based on solving the block linear system $AX=B$. Algorithm performance, i.e., time to solution, is improved by using the matrix $A$ in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.