Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we introduce a new approach to improve the preciseness of the standard Quantum Fourier Transform. The presented Quantum-SVD algorithm is based on the singular value dec...

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...

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...

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...

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...

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...

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...

The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and then show the central role of SVD in matrices. Using majorization theory, we consider variational principles of singular values and eigenvalues. Built on SVD...