Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts

Details Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts

2006-04-03

arxiv.org/abs/gr-qc/0604005v3

Class.Quant.Grav.23:S673-S686,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 5 figures

Scientific paper

10.1088/0264-9381/23/19/S05

Coherent techniques for searches of gravitational-wave bursts effectively combine data from several detectors, taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most natural way to combine data, which can also be used without prior knowledge of the signal. Recent studies however have shown that straightforward application of the maximum likelihood method to gravitational waves with unknown waveforms can lead to inconsistencies and unphysical results such as discontinuity in the residual functional, or divergence of the variance of the estimated waveforms for some locations in the sky. So far the solutions to these problems have been based on rather different physical arguments. Following these investigations, we now find that all these inconsistencies stem from rank deficiency of the underlying network response matrix. In this paper we show that the detection of gravitational-wave bursts with a network of interferometers belongs to the category of ill-posed problems. We then apply the method of Tikhonov regularization to resolve the rank deficiency and introduce a minimal regulator which yields a well-conditioned solution to the inverse problem for all locations on the sky.

Affiliated with

Also associated with

No associations

Rating

Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-444013