Parallel Algorithms for Triangular Periodic Sylvester-Type Matrix Equations
Parallel Algorithms for Triangular Periodic Sylvester-Type Matrix Equations
复制标题
三角周期Sylvester型矩阵方程的并行算法
DOI：
10.1007/978-3-540-85451-7_83
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
B. Kågström
中科院分区：
文献类型：
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作者：
Per Andersson;R. Granat;Isak Jonsson;B. Kågström
我们提出了三角周期Sylvester型矩阵方程的并行算法，概念上是第三步的周期Bartels-Stewart-like的解决方案的方法一般周期Sylvester型矩阵方程的基础上的变量的周期Schur分解。所提出的算法的设计和实现的框架中最近开发的HPC库SCASY和基于显式块，2维块循环数据分布和波前样遍历的右手边矩阵。高性能是通过丰富使用3级BLAS操作获得的。它还演示了如何将SCASY关于通信和准三角系数矩阵的处理的几个重要的关键概念推广到周期性的情况。最后给出了在一个分布式内存Linux集群上的实验结果。
We present parallel algorithms for triangular periodic Sylves-ter-type matrix equations, conceptually being the third step of a periodic Bartels–Stewart-like solution method for general periodic Sylvester-type matrix equations based on variants of the periodic Schur decomposition. The presented algorithms are designed and implemented in the framework of the recently developed HPC library SCASY and are based on explicit blocking, 2-dimensional block cyclic data distribution and a wavefront-like traversal of the right hand side matrices. High performance is obtained by rich usage of level 3 BLAS operations. It is also demonstrated how several important key concepts of SCASY regarding communications and the treatment of quasi-triangular coefficient matrices are generalized to the periodic case. Some experimental results from a distributed memory Linux cluster demonstrate are also presented.