Iterative refinement for linear systems and LAPACK
Iterative refinement for linear systems and LAPACK
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DOI：
10.1093/imanum/17.4.495
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发表时间：
1997-10-01
影响因子：
2.1
通讯作者：
Higham, NJ
中科院分区：
文献类型：
--
作者：
Higham, NJ
在1940年代，在台式计算器和计算机上使用了改进线性系统计算的解决方案的迭代精炼技术，并且仍然很受欢迎。在1990年代，迭代精致效果很好，在软件库中得到了支持，特别是在拉帕克（Lapack）。尽管在浮点算术中迭代精致的行为众所周知，但现有的理论不足以证明在实施其实施的所有Lapack例程中使用固定精确的迭代精炼是合理的。我们提出的分析提供了Lapack所需的理论支持。该分析涵盖了混合精度和固定精度的迭代精制，并具有任意数量的迭代，仅在基础求解器上是一个一般假设，并且相对较短。我们确定了一些剩余的开放问题。
The technique of iterative refinement for improving the computed solution to a linear system was used on desk calculators and computers in the 1940s and has remained popular. In the 1990s iterative refinement is well,supported in software libraries, notably in LAPACK. Although the behaviour of iterative refinement in floating point arithmetic is reasonably well understood, the existing theory is not sufficient to justify the use of fixed precision iterative refinement in all the LAPACK routines in which it is implemented. We present analysis that provides the theoretical support needed for LAPACK. The analysis covers both mixed and fixed precision iterative refinement with an arbitrary number of iterations, makes only a general assumption on the underlying solver, and is relatively short. We identify some remaining open problems.