# Fast power spectrum estimation

@article{Pen2003FastPS, title={Fast power spectrum estimation}, author={Ue-li Pen}, journal={Monthly Notices of the Royal Astronomical Society}, year={2003}, volume={346}, pages={619-626} }

We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N log N), compared to the standard brute force approach which costs O(N 3 ). The procedure retains this speed on the full sky and for ill-conditioned matrices. It is applicable to galaxy power spectra, cosmic microwave background (CMB), polarization and weak lensing data. We present a mathematical convergence analysis…

## 20 Citations

Hybrid estimation of cosmic microwave background polarization power spectra

- Physics
- 2006

This paper generalizes the hybrid power spectrum estimation method developed in a previous paper to the estimation of polarization power spectra of the cosmic microwave background radiation. The…

Myths and truths concerning estimation of power spectra: the case for a hybrid estimator

- Physics
- 2003

It is widely believed that maximum-likelihood estimators must be used to provide optimal estimates of power spectra. Since such estimators require the inversion and multiplication of N d x N d…

Cosmic microwave background power spectrum estimation with non-circular beam and incomplete sky coverage

- Physics
- 2009

Over the last decade, measurements of the cosmic microwave background (CMB) anisotropy have spearheaded the remarkable transition of cosmology into a precision science. However, addressing the…

CMB power spectrum estimation using noncircular beams

- Physics
- 2004

The measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy have proved crucial to the emergence of cosmology as a precision science in recent years. In this…

Reconstruction of the One-Point Distribution of Convergence from Weak Lensing by Large-Scale Structure

- Physics
- 2005

Weak-lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps.…

Fast n-point correlation functions and three-point lensing application

- Computer Science, PhysicsArXiv
- 2003

A new algorithm to rapidly compute the two-point, three-point and n -point correlation functions in roughly O( N log N ) time for N particles, instead of O( n n ) as required by brute force approaches.

Non-Circular beam correction to the CMB power spectrum

- Physics
- 2006

Abstract In the era of high precision CMB measurements, systematic effects are beginning to limit the ability to extract subtler cosmological information. The non-circularity of the experimental beam…

Optimizing the computation of n-point correlations on large-scale astronomical data

- Computer Science2012 International Conference for High Performance Computing, Networking, Storage and Analysis
- 2012

A highly-tuned npcf computation code is presented that enables a much larger 3-point correlation computation on the galaxy distribution than was previously possible, and a detailed performance evaluation on many different architectures is shown.

A method for 21 cm power spectrum estimation in the presence of foregrounds

- Physics
- 2011

The technique of 21 cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However,…

Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling

- Physics
- 2004

We describe an efficient and exact method that enables global Bayesian analysis of cosmic microwave background (CMB) data. The method reveals the joint posterior density (or likelihood for flat…

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