Related papers: Use of Singular-Value Decomposition in Gravitation…

The main problem that we will face in the data analysis for continuous gravitational-wave sources is processing of a very long time series and a very large parameter space. We present a number of analytic and numerical tools that can be…

We present a new multivariate regression model for analysis and parameter estimation of gravitational waves observed from well but not perfectly modeled sources such as core-collapse supernovae. Our approach is based on a principal…

The singular value decomposition is arguably one of the most fundamental results in linear algebra. While rigorous proof of this result is of importance, equally important is the motivation in the applied settings. We provide a lively and…

Model waveforms are used in gravitational wave data analysis to detect and then to measure the properties of a source by matching the model waveforms to the signal from a detector. This paper derives accuracy standards for model waveforms…

The investigation into the scattering of plane waves by a periodic array of parallel cylinders utilizes the method of cylindrical wave decomposition, thereby reducing the problem complexity to a series of linear algebraic equations. This…

This document proposes data formats to exchange numerical relativity results, in particular gravitational waveforms. The primary goal is to further the interaction between gravitational-wave source modeling groups and the gravitational-wave…

Gravitational wave generation by a strong shock wave in the interaction of high power laser with matter is analyzed in linear approximation of gravitational theory. The analytical formulas and estimates are derived for the metric…

This paper aims to develop a simple procedure to reduce and control the condition number of random matrices, and investigate the effect on the persistent homology (PH) of point clouds of well- and ill-conditioned matrices. For a square…

We quantify the advantages of a recently proposed data processing technique to search for continuous gravitational wave (GW) signals from isolated rotating asymmetric neutron stars in data measured by ground-based GW interferometers. This…

In singular value decomposition (SVD) of a complex matrix A, the singular vectors or the eigenvectors of AA{\dag} and A{\dag}A are unique up to complex phase factors. Thus, the two unitary matrices in SVD are unique up to diagonal matrices…

Orthogonal decomposition of tensors is a generalization of the singular value decomposition of matrices. In this paper, we study the spectral theory of orthogonally decomposable tensors. For such a tensor, we give a description of its…

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…

Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…

In this paper, we derive new model formulations for computing generalized singular values of a Grassman matrix pair. These new formulations make use of truncated filter matrices to locate the $i$-th generalized singular value of a Grassman…

The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…

In this paper two ways to compute singular values are presented which use Cholesky decomposition as their basic operation.

This thesis is devoted to the investigations of gravitational wave (GW) data analysis from a continuous source e.g. a pulsar, a binary star system. The first Chapter is an introduction to gravitational wave and second Chapter is on the data…

Two methods to decompose block matrices analogous to Singular Matrix Decomposition are proposed, one yielding the so called economy decomposition, and other yielding the full decomposition. This method is devised to avoid handling matrices…

Images are a substantial portion of the internet, making efficient compression important for reducing storage and bandwidth demands. This study investigates the use of Singular Value Decomposition and low-rank matrix approximations for…

This paper introduces the use of Principal Component Analysis as a method to decompose the waveform catalogues to produce a set of orthonormal basis vectors. We apply this method to a set of supernova waveforms and compare the basis vectors…