Golub and Loan (1980) presented a numerically-stable TLS algorithm which utilizes the singular value decomposition (SVD). Subsequent refinements to the method predominantly use SVD, and much of the current literature emphasizes stabilization of the inverse and implicit model regularization by SVD truncation (Fierro et al., 1997). Because it is numerically intensive, however, the SVD generally p...

The Singular Value Decomposition (SVD) is a fundamental algorithm used to understand the structure of data by providing insight into the relationship between the row and column factors. SVD aims to approximate a rectangular data matrix, given some rank restriction, especially lower rank approximation. In practical data analysis, however, outliers and missing values maybe exist that restrict the...

Singular value decomposition (SVD) is a useful multivariate technique for dimension reduction. It has been successfully applied to analyze microarray data, where the eigen vectors are called eigen-genes/arrays. One weakness associated with the SVD is the interpretation. The eigen-genes are essentially linear combinations of all the genes. It is desirable to have sparse SVD, which retains the di...

We demonstrate an implementation for an approximate rank-k SVD factorization, combiningwell-known randomized projection techniques with previously implemented map/reduce solutions in order to compute steps of the random projection based SVD procedure, such QR and SVD. We structure the problem in a way that it reduces to Cholesky and SVD factorizations on k× k matrices computed on a single machi...

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

In this work we consider algorithms based on the Singular Value Decomposition (SVD) to approximate Lyapunov and Exponential Dichotomy spectra of dynamical systems. We review existing contributions, and propose new algorithms of the continuous SVD method. We present implementation details for the continuous SVD method, and illustrate on several examples the behavior of continuous (and also discr...

The text retrieval method using latent semantic indexing (LSI) technique with truncated singular value decomposition (SVD) has been intensively studied in recent years. The SVD reduces the noise contained in the original representation of the term–document matrix and improves the information retrieval accuracy. Recent studies indicate that SVD is mostly useful for small homogeneous data collect...

Singular Value Decomposition (SVD) is of great significance in theory development of mathematics and statistics. In this paper we propose the SVD for 3-dimensional (3-D) matrices and extend it to the general Multidimensional Matrices (MM). We use the basic operations associated with MM introduced by Solo to define some additional aspects of MM. We achieve SVD for 3-D matrix through these MM ope...