Stability of Parallel Triangular System Solvers
Stability of Parallel Triangular System Solvers
复制标题
平行三角系统求解器的稳定性
DOI：
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发表时间：
1995
影响因子：
3.1
通讯作者：
N. Higham
中科院分区：
文献类型：
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作者：
N. Higham
已经提出了几种平行算法用于三角系统的溶液。这里分析了其中四个的稳定性：一种粉丝算法，块消除方法，基于基于矩阵倒数的分解功率系列扩展的方法，以及基于分隔和征服矩阵反转技术的方法。得出了新的向前误差和残留界限，包括对风扇中的算法对Sameh和Brent的边界的改进。确定了一个正向误差绑定，不仅适用于此处描述的所有方法，还可以确定不依赖代数取消的任何三角方程求解器；在结合的含义中，对于某些特殊类型的三角形系统，任何此类方法都非常准确。
Several parallel algorithms have been proposed for the solution of triangular systems. The stability of four of them is analysed here: a fan-in algorithm, a block elimination method, a method based on a factorized power series expansion of the matrix inverse, and a method based on a divide and conquer matrix inversion technique. New forward error and residual bounds are derived, including an improvement on the bounds of Sameh and Brent for the fan-in algorithm. A forward error bound is identified that holds not only for all the methods described here, but for any triangular equation solver that does not rely on algebraic cancellation; among the implications of the bound is that any such method is extremely accurate for certain special types of triangular systems.