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...

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...

Introduction: Brain visual evoked potential (VEP) signals are commonly known to be accompanied by high levels of background noise typically from the spontaneous background brain activity of electroencephalography (EEG) signals. Material and Methods: A model based on dyadic filter bank, discrete wavelet transform (DWT), and singular value decomposition (SVD) was developed to analyze the raw data...

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...

Objectives: Hypertension is a major risk factor for white matter hyperintensities (WMH), lacunes, cerebral microbleeds, and perivascular spaces, which are MRI markers of cerebral small vessel disease (SVD). Studies have shown associations between these individual MRI markers and cognitive functioning and decline. Recently, a "total SVD score" was proposed in which the different MRI markers were...

demonstrated significantly more severe SVD-associated pathology compared to controls, which suggests that SVD may have a role in the pathophysiology of PD [12]. Another longitudinal study by Foo et al. demonstrated that progression of SVD was associated with significant cortical thinning in the frontoparietal regions with concomitant decline in memory, executive functions, and motor functions i...