scholarly journals An Accelerated Accuracy-enhanced Randomized Singular Value Decomposition for Factorizing Matrices with Low-rank Structure

2020 ◽  
Vol 9 (4) ◽  
pp. 64
Author(s):  
Joseph Roger Arhin ◽  
Francis Sam ◽  
Kenneth Coker ◽  
Toufic Seini
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Low Rank ◽  
Value Decomposition

A Control Loop Structure Based on Singular Value Decomposition for Input-Coupled Systems

2011 ◽  
Author(s):  
Ryder C. Winck ◽  
Wayne J. Book
Keyword(s):  
Singular Value Decomposition ◽  
Current Control ◽  
Singular Value ◽  
Coupled Systems ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Column System ◽  
Input Design ◽  
Actuator Control ◽  
Value Decomposition

This paper introduces a control structure based on the singular value decomposition (SVD) to control multiple subsystems with reduced inputs. The SVD System permits simultaneous, dependent control of sets of subsystems coupled by a row-column input design. The use of the SVD differs from previous applications because it is used to obtain a low-rank approximation of desired inputs. The row-column system allows many actuators to be controlled by a few inputs. Current control methods using the row-column system rely on scheduling techniques that permit independent actuator control but are too slow for many applications. The inspiration for this new control construct is a pin array human machine interface, called Digital Clay. Some useful properties of the SVD will be discussed and the SVD System will be described and demonstrated in a simulation of Digital Clay.

An Improved Seismic Data Completion Algorithm using Low-Rank Tensor Optimization: Cost Reduction and Optimal Data Orientation

Geophysics ◽  
2021 ◽  
pp. 1-88
Author(s):  
Jonathan Popa ◽  
Susan E. Minkoff ◽  
Yifei Lou
Keyword(s):  
Fourier Transform ◽  
Singular Value Decomposition ◽  
Seismic Data ◽  
Convex Sets ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Low Rank ◽  
Traditional Methods ◽  
Value Decomposition ◽  
Conjugate Symmetry

Seismic data are often incomplete due to equipment malfunction, limited source and receiver placement at near and far offsets, and missing cross-line data. Seismic data contain redundancies as they are repeatedly recorded over the same or adjacent subsurface regions, causing the data to have a low-rank structure. To recover missing data one can organize the data into a multidimensional array or tensor and apply a tensor completion method. We can increase the effectiveness and efficiency of low-rank data reconstruction based on the tensor singular value decomposition (tSVD) by analyzing the effect of tensor orientation and exploiting the conjugate symmetry of the multidimensional Fourier transform. In fact, these results can be generalized to any order tensor. Relating the singular values of the tSVD to those of a matrix leads to a simplified analysis, revealing that the most square orientation gives the best data structure for low-rank reconstruction. After the first step of the tSVD, a multidimensional Fourier transform, frontal slices of the tensor form conjugate pairs. For each pair a singular value decomposition can be replaced with a much cheaper conjugate calculation, allowing for faster computation of the tSVD. Using conjugate symmetry in our improved tSVD algorithm reduces the runtime of the inner loop by 35% to 50%. We consider synthetic and real seismic datasets from the Viking Graben Region and the Northwest Shelf of Australia arranged as high-dimensional tensors. We compare tSVD based reconstruction to traditional methods, projection onto convex sets and multichannel singular spectrum analysis, and see that the tSVD based method gives similar or better accuracy and is more efficient, converging with runtimes that are an order of magnitude faster than the traditional methods. Additionally, we verify the most square orientation improves recovery for these examples by 10-20% compared to the other orientations.

Automotive’s Vibration Analysis by Dynamic Impedance Method (Available Criterion in Use of Singular Value Decomposition)

1995 ◽  
Vol 7 (4) ◽  
pp. 274-279 ◽  
Author(s):  
Masanobu Nakamura ◽  
◽  
Akio Nagamatsu ◽  
Takeshi Sawanobori ◽  
Yoshinobu Kamada ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Direct Method ◽  
Decomposition Theorem ◽  
Singular Value ◽  
Low Rank ◽  
Impedance Method ◽  
Automotive Systems ◽  
Dynamic Impedance ◽  
Generalized Matrix ◽  
Value Decomposition

This paper presents the results of numerical simulations to mix noise generated with random numbers in response signals to show that the use of the Singular Value Decomposition theorem to calculate a low rank generalized matrix inverse can reduce the influence of noise on synthesized results obtained with a dynamic impedance method. The effectiveness of this approach over the direct method is confirmed . A new procedure is also proposed for determining the applicability of the SVD theorem. An application of the proposed approach is presented to demonstrate its usefulness in analyzing vibration problems in automotive systems.

A QUINTET SINGULAR VALUE DECOMPOSITION THROUGH EMPIRICAL MODE DECOMPOSITIONS

2014 ◽  
Vol 06 (02n03) ◽  
pp. 1450010
Author(s):  
MIN-SUNG KOH
Keyword(s):  
Singular Value Decomposition ◽  
Speech Enhancement ◽  
Singular Values ◽  
Singular Value ◽  
Diagonal Matrix ◽  
Low Rank ◽  
Orthogonal Matrices ◽  
Low Rank Approximations ◽  
Single Matrix ◽  
Value Decomposition

A particular quintet singular valued decomposition (Quintet-SVD) is introduced in this paper via empirical mode decompositions (EMDs). The Quintet-SVD results in four specific orthogonal matrices with a diagonal matrix of singular values. Furthermore, this paper shows relationships between the Quintet-SVD and traditional SVD, generalized low rank approximations of matrices (GLRAM) of one single matrix, and EMDs. One application of the Quintet-SVD for speech enhancement is shown and compared with an application of traditional SVD.

scholarly journals Principal Component Analysis and Its Derivation From Singular Value Decomposition

2019 ◽  
Vol 8 (2) ◽  
pp. 183
Author(s):  
Orumie, Ukamaka Cynthia ◽  
Ogbonna Onyinyechi
Keyword(s):  
Principal Component Analysis ◽  
Singular Value Decomposition ◽  
Principal Component ◽  
Component Analysis ◽  
Singular Value ◽  
Low Rank ◽  
Singular Value Decomposition Method ◽  
Daunting Task ◽  
Low Rank Approximations ◽  
Value Decomposition

Generally, today data analysts and researchers are often faced with a daunting task of reducing high dimensional datasets as large volume of data can be easily generated given the explosive activities of the internet. The most widely used tools for data reduction is the principal component analysis. Merely in some cases, the singular value decomposition method is applied. The study examined the application and theoretical framework of these methods in terms of its linear algebra foundation. The study discovered that the SVD method is a more robust and general method for a change of basis and low rank approximations. But.in terms of application, the PCA method is easy to interpret as illustrated in the work.

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