scholarly journals Induced Dimension Reduction Method for Solving Linear Matrix Equations

2016 ◽  
Vol 80 ◽  
pp. 222-232 ◽  
Author(s):  
Reinaldo Astudillo ◽  
Martin B. van Gijzen
Keyword(s):  
Dimension Reduction ◽  
Reduction Method ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Dimension Reduction Method ◽  
Linear Matrix Equations

scholarly journals A generalized inverse for matrices

1955 ◽  
Vol 51 (3) ◽  
pp. 406-413 ◽  
Author(s):  
R. Penrose
Keyword(s):  
Unique Solution ◽  
Spectral Decomposition ◽  
Generalized Inverse ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Singular Matrix ◽  
Rectangular Matrix ◽  
New Type ◽  
Linear Matrix Equations

This paper describes a generalization of the inverse of a non-singular matrix, as the unique solution of a certain set of equations. This generalized inverse exists for any (possibly rectangular) matrix whatsoever with complex elements. It is used here for solving linear matrix equations, and among other applications for finding an expression for the principal idempotent elements of a matrix. Also a new type of spectral decomposition is given.

scholarly journals Multidimensional Scaling-Based Data Dimension Reduction Method for Application in Short-Term Traffic Flow Prediction for Urban Road Network

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yi Zhao ◽  
Satish V. Ukkusuri ◽  
Jian Lu
Keyword(s):  
Dimension Reduction ◽  
Traffic Flow ◽  
Reduction Method ◽  
Prediction Models ◽  
Urban Traffic ◽  
Dimension Reduction Method ◽  
Short Term ◽  
Urban Road ◽  
Traffic Flow Prediction ◽  
Flow Prediction

This study develops a multidimensional scaling- (MDS-) based data dimension reduction method. The method is applied to short-term traffic flow prediction in urban road networks. The data dimension reduction method can be divided into three steps. The first is data selection based on qualitative analysis, the second is data grouping using the MDS method, and the last is data dimension reduction based on a correlation coefficient. Backpropagation neural network (BPNN) and multiple linear regression (MLR) models are employed in four kinds of urban traffic environments to test whether the proposed method improves the prediction accuracy of traffic flow. The results show that prediction models using traffic data after dimension reduction outperform the same prediction models using other datasets. The proposed method provides an alternative to existing models for urban traffic prediction.

scholarly journals The optimal convergence factor of the gradient based iterative algorithm for linear matrix equations

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 607-613 ◽  
Author(s):  
Xiang Wang ◽  
Dan Liao
Keyword(s):  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Convergence Factor ◽  
Gradient Based ◽  
Gradient Type ◽  
And Mathematics ◽  
Computers And Mathematics ◽  
Linear Matrix Equations

A hierarchical gradient based iterative algorithm of [L. Xie et al., Computers and Mathematics with Applications 58 (2009) 1441-1448] has been presented for finding the numerical solution for general linear matrix equations, and the convergent factor has been discussed by numerical experiments. However, they pointed out that how to choose a best convergence factor is still a project to be studied. In this paper, we discussed the optimal convergent factor for the gradient based iterative algorithm and obtained the optimal convergent factor. Moreover, the theoretical results of this paper can be extended to other methods of gradient-type based. Results of numerical experiments are consistent with the theoretical findings.

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