Related papers: Use of Singular-Value Decomposition in Gravitation…
We investigate the application of the singular value decomposition to compact-binary, gravitational-wave data-analysis. We find that the truncated singular value decomposition reduces the number of filters required to analyze a given region…
Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two…
Gravitational-wave searches for the merger of compact binaries use matched-filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high…
The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the…
Compact binary systems with total masses between tens and hundreds of solar masses will produce gravitational waves during their merger phase that are detectable by second-generation ground-based gravitational-wave detectors. In order to…
Several large-scale gravitational wave (GW) interferometers have achieved long term operation at design sensitivity. Questions arise on how to best combine all available data from detectors of different sensitivities for detection,…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
Matched-filtering for the identification of compact object mergers in gravitational-wave antenna data involves the comparison of the data stream to a bank of template gravitational waveforms. Typically the template bank is constructed from…
The detection of gravitational waves from compact binaries relies on a computationally burdensome processing of gravitational-wave detector data. The parameter space of compact-binary-coalescence gravitational waves is large and optimal…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
We develop an Iterative version of the Singular Value Decomposition (ISVD) that jointly analyzes a finite number of data matrices to identify signals that correlate among the rows of matrices. It will be illustrated how the supervised…
Accurate parameter estimation of gravitational waves from coalescing compact binary sources is a key requirement for gravitational-wave astronomy. Evaluating the posterior probability density function of the binary's parameters (component…
Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…
In signal processing and identification, generalized singular value decomposition (GSVD), related to a sequence of matrices in product/quotient form are essential numerical linear algebra tools. On behalf of the growing demand for efficient…
The detection of gravitational wave usually requires to match the measurement data with a large number of templates, which is computationally very expensive. Compressed sensing methods allow one to match the data with a small number of…
Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the…
Singular spectrum analysis is developed as a nonparametric spectral decomposition of a time series. It can be easily extended to the decomposition of multidimensional lattice-like data through the filtering interpretation. In this…
Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although…
Matrix factorizations in dual number algebra, a hypercomplex system, have been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves…
Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…