Related papers: Use of Singular-Value Decomposition in Gravitation…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
A novel methodology for analysing the relation between the energy density in gravitational waves and primordial power spectra is developed. Focusing on scalar-induced gravitational radiation, this methodology is applied to a number of…
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…
The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and…
We present a generalisation of the pseudoinverse operation to pairs of matrices, as opposed to single matrices alone. We note the fact that the Singular Value Decomposition can be used to compute the ordinary Moore-Penrose pseudoinverse. We…
This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under…
We present a progress report on the use of normalizing flows for generating gauge field configurations in pure SU(N) gauge theories. We discuss how the singular value decomposition can be used to construct gauge-invariant quantities, which…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Because of the small strain amplitudes of gravitational-wave (GW) signals, unveiling them in the presence of detector/environmental noise is challenging. For visualizing the signals and extracting its waveform for a comparison with…
Pure gravitational plane waves are considered as a special case of spacetimes with two commuting spacelike Killing vector fields. Starting with a midisuperspace that describes this kind of spacetimes, we introduce gauge-fixing and symmetry…
A filter based on the Hankel Lanczos Singular Value Decomposition (HLSVD) technique is presented and applied for the first time to X-ray diffraction (XRD) data. Synthetic and real powder XRD intensity profiles of nanocrystals are used to…
Astrometric observations can, in principle, be used to detect gravitational waves. In this paper we give a practical overview of the gravitational wave effects which can be expected specifically in small-field astrometric data. Particular…
We present a new method of wavelet packet decomposition to be used in gravitational wave detection. An issue in wavelet analysis is what is the time-frequency resolution which is best suited to analyze data when in quest of a signal of…
In this paper, we review the theoretical basis for generation of gravitational waves and the detection techniques used to detect a gravitational wave. To materialize this goal in a thorough way we first start with a mathematical background…
Modes generally provide an economical description of waves, reducing complicated wave functions to finite numbers of mode amplitudes, as in propagating fiber modes and ideal laser beams. But finding a corresponding mode description for…
We describe a new method for extracting gravitational wave signals from pulsar timing data. We show that any gravitational wave signal can be decomposed into an orthogonal set of sky maps, with the number of maps equal to the number of…
Gravitational wave (GW) observations probe both a diffuse, stochastic gravitational wave background (SGWB) as well as individual cataclysmic events such as the merger of two compact objects. The detection and description of the…
In this paper, some new results on the distribution of the generalized singular value decomposition (GSVD) are presented.
We propose a new hypermatrix singular value decomposition based upon the spectral decomposition of the symmetric products of transposes.
We propose a data processing technique that allows searches for a stochastic background of gravitational radiation with data from a single detector. Our technique exploits the difference between the coherence time of the gravitational wave…