Related papers: Use of Singular-Value Decomposition in Gravitation…
Gravitational waves (GWs) hold great potential for an unobscured view of protoneutron stars (PNSs) formed as a result of stellar collapses. While waiting for discovery, deepening the understanding of GW emission in theory is beneficial for…
The traditional method of computing singular value decomposition (SVD) of a data matrix is based on a least squares principle, thus, is very sensitive to the presence of outliers. Hence the resulting inferences across different applications…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
This is an introductory survey, from a geometric perspective, on the Singular Value Decomposition (SVD) for real matrices, focusing on the role of the Terracini Lemma. We extend this point of view to tensors, we define the singular space of…
Various coefficients of the 3.5 post-Newtonian (PN) phasing formula of non-spinning compact binaries moving in circular orbits is fully characterized by the two component masses. If two of these coefficients are independently measured, the…
Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are available, such as for ground based and…
In this paper, we study the properties of gravitational waves in the scalar-tensor-vector gravity theory. The polarizations of the gravitational waves are investigated by analyzing the relative motion of the test particles. It is found that…
Stochastic background gravitational waves have not yet been detected by ground-based laser interferometric detectors, but recent improvements in detector sensitivity have raised considerable expectations for their eventual detection.…
The generalized singular value decomposition (GSVD) of a matrix pair $\{A, L\}$ with $A\in\mathbb{R}^{m\times n}$ and $L\in\mathbb{R}^{p\times n}$ generalizes the singular value decomposition (SVD) of a single matrix. In this paper, we…
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…
Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
It is known that singular values of idempotent matrices are either zero or larger or equal to one \cite{HouC63}. We state exactly how many singular values greater than one, equal to one, and equal to zero there are. Moreover, we derive a…
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general…
We present a matrix version of a known method of constructing common eigenvectors of two diagonalizable commuting matrices, thus enabling their simultaneous diagonalization. The matrices may have simple eigenvalues of multiplicity greater…
Propagation of weak gravitational waves, when a dynamical four-form is around, has been investigated. Exact, self-consistent solutions corresponding to plane, monochromatic gravitational waves have been studied.
Singular Value Decomposition (SVD) has recently emerged as a new paradigm for processing different types of images. SVD is an attractive algebraic transform for image processing applications. The paper proposes an experimental survey for…
A method is presented to generalize the power detectors for short bursts of gravitational waves that have been developed for single interferometers so that they can optimally process data from a network of interferometers. The performances…
We report on phase-shifted holographic interferogram demodulation by singular value decomposition. Numerical processing of optically-acquired interferograms over several modulation periods was performed in two steps : 1- rendering of…