Solving linear equations with messenger-field and conjugate gradient techniques: An application to CMB data analysis

被引:5
作者
Papez, J. [1 ]
Grigori, L. [1 ]
Stompor, R. [2 ]
机构
[1] Univ Paris Diderot SPC, Sorbonne Univ, Lab Jacques Louis Lions, Equipe ALPINES,CNRS,INRIA Paris, Paris, France
[2] Univ Paris Diderot, AstroParticule & Cosmol, Sorbonne Paris Cite, CNRS,IN2P3,CEA Irfu,Obs Paris, Paris, France
基金
欧盟地平线“2020”;
关键词
methods: numerical; cosmic background radiation;
D O I
10.1051/0004-6361/201832987
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
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.
引用
收藏
页数:14
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