Efficient newton–raphson/singular value decomposition‐based optimization scheme with dynamically updated critical condition number for rapid convergence of weighted histogram analysis method equations

2019 ◽  
Vol 41 (3) ◽  
pp. 240-246
Author(s):  
Roma Mukhopadhyay ◽  
Marat R. Talipov
Keyword(s):  
Singular Value Decomposition ◽  
Condition Number ◽  
Singular Value ◽  
Analysis Method ◽  
Optimization Scheme ◽  
Rapid Convergence ◽  
Newton Raphson ◽  
Value Decomposition ◽  
Weighted Histogram ◽  
Weighted Histogram Analysis

The Algebraic Operation of SVD

2011 ◽  
Author(s):  
Gidon Eshel
Keyword(s):  
Data Analysis ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Algebraic Operation ◽  
Analysis Method ◽  
Data Analysis Method ◽  
Value Decomposition ◽  
Data Matrices

Chapter 4 discussed the eigenvalue/eigenvector diagonalization of a matrix. Perhaps the biggest problem for this to be very useful in data analysis is the restriction to square matrices. It has already been emphasized time and again that data matrices, unlike dynamical operators, are rarely square. The algebraic operation of the singular value decomposition (SVD) is the answer. Note the distinction between the data analysis method widely known as SVD and the actual algebraic machinery. The former uses the latter, but is not the latter. This chapter describes the method. Following the introduction to SVD, it provides some examples and applications.

Vibration load and transfer path identification of vehicle using inverse matrix method based on singular value decomposition

2019 ◽  
Vol 234 (6) ◽  
pp. 1703-1713
Author(s):  
Chao Yang ◽  
Yansong Wang ◽  
Hui Guo ◽  
Jiang Lv ◽  
Ningning Liu ◽  
...  
Keyword(s):  
Transfer Function ◽  
Singular Value Decomposition ◽  
Condition Number ◽  
Singular Value ◽  
Reference Points ◽  
Load Identification ◽  
Transfer Function Matrix ◽  
Key Points ◽  
Value Decomposition ◽  
Function Matrix

Based on the theory of inverse transfer matrix, a novel method for simultaneous load identification of vehicle vibration is presented in this paper. Some response, excitation, reference points (called key points) and their transfer paths, which have severe effects on the vibration of a whole vehicle, are defined. The transfer functions among the key points are measured by experiments, and thereby a transfer function matrix of vehicle vibration is established. To solve ill-conditioning problem in the transfer function matrix, the methodology of singular value decomposition is introduced into matrix inversion in the excitation load identification. To reduce the identification error, four transfer function matrices with different reference points and condition numbers are selected and discussed. The results show that the more the reference points are, the smaller the condition number of transfer function matrix is, the higher the accuracy of excitation load identification. The transfer function matrix with minimum condition number is used to identify the excitation loads at the vehicle key points. Experimental verifications suggest that the newly proposed method is effective and feasible for excitation load identification of vehicle vibration. Using the identified excitation loads, furthermore, the vibration causes of the steering wheel and seat rail are obtained, which is helpful for improving vibration performance of the sample vehicle. In applications, the excitation load identification method proposed in this paper may be applied not only to other types of vehicle, but also to other complex electromechanical products for load identification in engineering.

Factor analysis of ambiguity in geophysics

Geophysics ◽  
1994 ◽  
Vol 59 (7) ◽  
pp. 1083-1091 ◽  
Author(s):  
Simone G. C. Fraiha ◽  
João B. C. Silva
Keyword(s):  
Factor Analysis ◽  
Singular Value Decomposition ◽  
Finite Number ◽  
Analytical Methods ◽  
Decomposition Analysis ◽  
Singular Value ◽  
Analysis Method ◽  
Singular Value Decomposition Analysis ◽  
Value Decomposition

We present an empirical ambiguity analysis method based on a finite number of acceptable solutions that are representative of the ambiguity region. These solutions are submitted to a Q‐mode factor analysis that indicates which parameters are ambiguous and their ambiguity range. We illustrate, with a synthetic nonlinear example, that our method is more effective than singular value decomposition analysis in producing an average trend of the ambiguity region. It requires less restrictive hypotheses and is more robust than analytical methods of ambiguity analysis, in the sense of being applicable to a broader class of problems.

scholarly journals Proposal of Golf Swing Analysis Method Using Singular Value Decomposition

Proceedings ◽  
2020 ◽  
Vol 49 (1) ◽  
pp. 91
Author(s):  
Kenta Matsumoto ◽  
Nobutaka Tsujiuchi ◽  
Akihito Ito ◽  
Hiroshi Kobayashi ◽  
Masahiko Ueda ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Motion Capture ◽  
Singular Value ◽  
Golf Swing ◽  
Motion Capture System ◽  
Analysis Method ◽  
Main Mode ◽  
Value Decomposition ◽  
The Relationship ◽  
Positional Data

We analyzed the relationship between the cooperative actions of golf swings and the differences in swing trajectory. To extract cooperative actions from different swings, we acquired swing data in an experiment on an experienced golfer who swung with two different trajectories. We measured the swings with motion capture system (VICON). We built an observance matrix from the collected positional data and conducted singular value decomposition (SVD) on it. The SVD yielded the cooperative actions as independent modes. Next, we compared the cooperative actions of different swing trajectories in the main mode. The results indicate that the analysis of the golf swing could be divided into a dominant behavior and an accompanying behavior.

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