Recursive Blocked Algorithms for Solving Periodic Triangular Sylvester-Type Matrix Equations
Recursive Blocked Algorithms for Solving Periodic Triangular Sylvester-Type Matrix Equations
复制标题
求解周期三角西尔维斯特型矩阵方程的递归分块算法
DOI：
10.1007/978-3-540-75755-9_65
复制
发表时间：
2006
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：
R. Granat;Isak Jonsson;B. Kågström
最近，Jonsson和Kågström提出了求解三角形单边和双边Sylvester型方程的递归分块算法。这种优雅而简单的技术支持自动变量阻塞，具有匹配当今HPC系统的内存层次结构的潜力。计算的主要部分作为第3级通用矩阵乘加（GEMM）操作来执行。我们推广并应用递归分块技术求解周期Sylvester型矩阵方程。连续递归分裂在三维数组上执行，其中第三维表示矩阵方程的周期性。
Recently, recursive blocked algorithms for solving triangular one-sided and two-sided Sylvester-type equations were introduced by Jonsson and Kågström. This elegant yet simple technique enables an automatic variable blocking that has the potential of matching the memory hierarchies of today’s HPC systems. The main parts of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We extend and apply the recursive blocking technique to solving periodic Sylvester-type matrix equations. Successive recursive splittings are performed on 3-dimensional arrays, where the third dimension represents the periodicity of a matrix equation.