Solving linear equations with messenger-field and conjugate gradient techniques: An application to CMB data analysis
- Sorbonne Univ., Alpines (France)
- Univ. Paris Diderot, Sorbonne Paris Cité (France)
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. In conclusion, 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.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1543829
- Journal Information:
- Astronomy and Astrophysics, Journal Name: Astronomy and Astrophysics Vol. 620; ISSN 0004-6361
- Publisher:
- EDP SciencesCopyright Statement
- Country of Publication:
- United States
- Language:
- English
| Bayesian optimisation for likelihood-free cosmological inference | text | January 2018 |
| Efficient Optimal Reconstruction of Linear Fields and Band-powers from Cosmological Data | text | January 2018 |
Wiener filtering and pure $\mathcal {E}/\mathcal {B}$ decomposition of CMB maps with anisotropic correlated noise
|
journal | September 2019 |
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