The Inversion Problem for Two Fold Photoelectron Counting Statistics

1975 ◽  
Vol 53 (13) ◽  
pp. 1215-1220 ◽  
Author(s):  
Julian Blake ◽  
Richard Barakat
Keyword(s):  
Parameter Estimation ◽  
Correlation Function ◽  
Singular Value Decomposition ◽  
General Structure ◽  
Coherence Time ◽  
Singular Value ◽  
Spectral Information ◽  
Inversion Problem ◽  
Counting Statistics ◽  
Value Decomposition

The extraction of spectral information from measurements of the full or clipped photoelectron correlation function is treated. Unlike previous treatments, the discussion here is not limited to counting times short compared to the coherence time of the light. The method of singular value decomposition is applied to the case where there is no prior knowledge of the spectrum. Parameter estimation is applied when the general structure of the spectrum is known.

scholarly journals Determination of Broadening Functions using the Singular Value Decomposition (SVD) Technique

1999 ◽  
Vol 170 ◽  
pp. 82-90 ◽  
Author(s):  
Slavek Rucinski
Keyword(s):  
Correlation Function ◽  
Singular Value Decomposition ◽  
Cross Correlation ◽  
Singular Value ◽  
Spectral Lines ◽  
Linear Inversion ◽  
Standard Tool ◽  
Contact Binaries ◽  
Value Decomposition

AbstractThe cross-correlation function (CCF) has become the standard tool for extraction of radial-velocity and broadening information from high resolution spectra. It permits integration of information which is common to many spectral lines into one function which is easy to calculate, visualize and interpret. However, the CCF is not the best tool for many applications where it should be replaced by the proper broadening function (BF). Typical applications requiring use of BFs rather than CCFs involve finding locations of star spots, studies of projected shapes of highly distorted stars such as contact binaries (as no assumptions can be made about BF symmetry or even continuity) and [Fe/H] metallicity determinations (good baselines and avoidance of negative lobes are essential). It is stressed that the CCFs are not broadening functions. This note concentrates on the advantages of determining BFs through the process of linear inversion, preferably accomplished using the singular value decomposition (SVD). Some basic examples of numerical operations are given in the IDL programming language.

scholarly journals USE OF SINGULAR-VALUE DECOMPOSITION IN GRAVITATIONAL-WAVE DATA ANALYSIS

2013 ◽  
Vol 23 ◽  
pp. 99-105
Author(s):  
DREW KEPPEL
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Singular Value Decomposition ◽  
Gravitational Wave ◽  
Computational Cost ◽  
Singular Value ◽  
Matched Filtering ◽  
Powerful Technique ◽  
Wave Data ◽  
Value Decomposition

Singular-value decomposition is a powerful technique that has been used in the analysis of matrices in many fields. In this paper, we summarize how it has been applied to the analysis of gravitational-wave data analysis. These include producing basis waveforms for matched filtering, decreasing the computational cost of searching for many waveforms, improving parameter estimation, and providing a method of waveform interpolation.

Signal and traveltime parameter estimation using singular value decomposition

Geophysics ◽  
2014 ◽  
Vol 79 (5) ◽  
pp. U1-U14 ◽  
Author(s):  
Bjørn Ursin ◽  
Michelângelo G. Silva ◽  
Milton J. Porsani
Keyword(s):  
Parameter Estimation ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition
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