Right after its invention in the late nineties, Frequency Domain Decomposition (FDD) identification technique became very popular operational modal analysis community due to simplicity and robustness. The underlying idea of this consists computing singular value decomposition Power Spectral Densities (PSDs) estimated from measured vibration responses with periodogram (also known as “Welch’s”) a...

In this paper, we examine a spectral clustering algorithm for similarity graphs drawn from a simple random graph model, where nodes are allowed to have varying degrees, and we provide theoretical bounds on its performance. The random graph model we study is the Extended Planted Partition (EPP) model, a variant of the classical planted partition model. The standard approach to spectral clusterin...

a r t i c l e i n f o a b s t r a c t This paper presents a new time domain noise reduction approach based on Singular Value Decomposition (SVD) technique. In the proposed approach, the noisy signal is initially represented in a Hankel Matrix. Then SVD is applied on the Hankel Matrix to divide the data into signal subspace and noise subspace. Since singular vectors are the span bases of the mat...

We demonstrate that an algorithm proposed by Drineas et. al. in [7] to approximate the singular vectors/values of a matrix A, is not only of theoretical interest but also a fast, viable alternative to traditional algorithms. The algorithm samples a small number of rows (or columns) of the matrix, scales them appropriately to form a small matrix S and computes the singular value decomposition (S...

The Fourier transform truncated on $$[-c,c]$$ has for a long time been analyzed as acting $$L^2(-1/b,1/b)$$ into $$L^2(-1,1)$$ and its right-singular vectors are the prolate spheroidal wave functions. This paper considers operator defined larger space $$L^2(\cosh (b|\cdot |))$$ which it remains injective. main purpose is (1) to provide nonasymptotic upper lower bounds singular values with simil...

In statistics and machine learning, people are often interested in the eigenvectors (or singular vectors) of certain matrices (e.g. covariance matrices, data matrices, etc). However, those matrices are usually perturbed by noises or statistical errors, either from random sampling or structural patterns. One usually employs Davis-Kahan sin θ theorem to bound the difference between the eigenvecto...

Applying smoothed aggregation multigrid (SA) to solve a nonsymmetric linear system, Ax = b, is often impeded by the lack of a minimization principle that can be used as a basis for the coarse-grid correction process. This paper proposes a Petrov-Galerkin (PG) approach based on applying SA to either of two symmetric positive definite (SPD) matrices, √ AtA or √ AAt. These matrices, however, are t...

The aim of this paper is to apply systematically to AdS 4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS 4 algebra and group. We give explicitly all singular (null) vectors ...

The aim of this paper is to apply systematically to AdS 4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS 4 algebra and group. We give explicitly all singular (null) vectors ...