Chebyshev acceleration of iterative refinement
Chebyshev acceleration of iterative refinement
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DOI：
10.1007/s11075-013-9750-7
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发表时间：
2014-07
影响因子：
2.1
通讯作者：
M. Arioli;J. Scott
中科院分区：
文献类型：
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作者：
M. Arioli;J. Scott
众所周知，FGMRES算法可以用作迭代精化的替代方案，并且在某些情况下，当迭代精化无法收敛时，FGMRES算法可以成功地计算向后稳定的解。在这项研究中，我们分析如何变形的Chebyshev算法也可以用来加速迭代细化，而不会损失数值稳定性，并在每次迭代的计算成本是小于FGMRES和仅略大于迭代细化。一个组件明智的错误分析的程序和选定的稀疏测试问题的数值试验，以证实理论。
It is well known that the FGMRES algorithm can be used as an alternative to iterative refinement and, in some instances, is successful in computing a backward stable solution when iterative refinement fails to converge. In this study, we analyse how variants of the Chebyshev algorithm can also be used to accelerate iterative refinement without loss of numerical stability and at a computational cost at each iteration that is less than that of FGMRES and only marginally greater than that of iterative refinement. A component-wise error analysis of the procedure is presented and numerical tests on selected sparse test problems are used to corroborate the theory.