Solving linear equations with messenger-field and conjugate gradient techniques: An application to CMB data analysis
Solving linear equations with messenger-field and conjugate gradient techniques: An application to CMB data analysis
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使用信使场和共轭梯度技术求解线性方程：CMB 数据分析的应用
DOI：
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发表时间：
2018
影响因子：
6.5
通讯作者：
R. Stompor
中科院分区：
文献类型：
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作者：
J. Papež;L. Grigori;R. Stompor
我们讨论线性系统求解器调用信使字段，并比较它们与（预处理）共轭梯度法。我们表明，信使场技术对应于一个适当的预处理的初始线性方程组的不动点迭代。然后，我们认为，一个共轭梯度求解器应用到相同的预处理系统，或等效的预处理共轭梯度求解器使用相同的预处理器和应用到原始系统，一般将确保至少有一个可比的，通常更好的性能方面的迭代收敛和时间的解决方案。我们说明我们的结论与两个常见的例子来自宇宙微波背景（CMB）的数据分析：维纳滤波和地图制作。此外，与CMB领域的标准知识相反，我们表明，预处理共轭梯度求解器的性能可以显着依赖于起始向量。这一观察似乎特别重要的情况下，地图制作的高信号-噪声比的天空地图，因此应该是相关的下一代的CMB实验。
We discuss linear system solvers invoking a messenger-field and compare them with (preconditioned) conjugate gradient approaches. We show that the messenger-field techniques correspond to fixed point iterations of an appropriately preconditioned initial system of linear equations. We then argue that a conjugate gradient solver applied to the same preconditioned system, or equivalently a preconditioned conjugate gradient solver using the same preconditioner and applied to the original system, will in general ensure at least a comparable and typically better performance in terms of the number of iterations to convergence and time-to-solution. We illustrate our conclusions with two common examples drawn from the cosmic microwave background (CMB) data analysis: Wiener filtering and map-making. In addition, and contrary to the standard lore in the CMB field, we show that the performance of the preconditioned conjugate gradient solver can depend significantly on the starting vector. This observation seems of particular importance in the cases of map-making of high signal-to-noise ratio sky maps and therefore should be of relevance for the next generation of CMB experiments.
DOI：
10.1088/0067-0049/187/1/212
发表时间：
2009-06
期刊：
The Astrophysical Journal Supplement Series
影响因子：
--
作者：
C. Cantalupo;J. Borrill;A. Jaffe;T. Kisner;R. Stompor
通讯作者：
C. Cantalupo;J. Borrill;A. Jaffe;T. Kisner;R. Stompor