Multiple Eigenvalues

2013 ◽  
pp. 51-71
Author(s):  
Yuli Eidelman ◽  
Israel Gohberg ◽  
Iulian Haimovici
Keyword(s):  
Multiple Eigenvalues

scholarly journals Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1522
Author(s):  
Anna Concas ◽  
Lothar Reichel ◽  
Giuseppe Rodriguez ◽  
Yunzi Zhang
Keyword(s):  
Iterative Methods ◽  
Adjacency Matrix ◽  
Lanczos Method ◽  
Power Method ◽  
Arnoldi Method ◽  
Multiple Eigenvalues ◽  
Computer Storage ◽  
Adjacency Matrices ◽  
Lanczos Methods ◽  
Perron Vector

The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude. It is well known that the Lanczos method typically requires fewer iterations than the power method to determine eigenvectors with the desired accuracy. However, the Lanczos method demands more computer storage, which may make it impractical to apply to very large problems. The present paper adapts the analysis by Blondel et al. to the Lanczos and restarted Lanczos methods. The restarted methods are found to yield fast convergence and to require less computer storage than the Lanczos method. Computed examples illustrate the theory presented. Applications of the Arnoldi method are also discussed.

scholarly journals On collision of multiple eigenvalues for matrix-valued Gaussian processes

2021 ◽  
Vol 502 (2) ◽  
pp. 125261
Author(s):  
Jian Song ◽  
Yimin Xiao ◽  
Wangjun Yuan
Keyword(s):  
Gaussian Processes ◽  
Multiple Eigenvalues

scholarly journals Axial Piston Pump Fault Diagnosis Method Based on Symmetrical Polar Coordinate Image and Fuzzy C-Means Clustering Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Wan-lu Jiang ◽  
Pei-yao Zhang ◽  
Man Li ◽  
Shu-qing Zhang
Keyword(s):  
Fault Diagnosis ◽  
Clustering Algorithm ◽  
Piston Pump ◽  
Axial Piston Pump ◽  
Fuzzy C Means ◽  
Multiple Eigenvalues ◽  
Polar Coordinate ◽  
Fuzzy C Means Clustering ◽  
Diagnosis Method ◽  
Axial Piston

In this paper, a fault diagnosis method based on symmetric polar coordinate image and Fuzzy C-Means clustering algorithm is proposed to solve the problem that the fault signal of axial piston pump is not intuitive under the time-domain waveform diagram. In this paper, the sampled vibration signals of axial piston pump were denoised firstly by the combination of ensemble empirical mode decomposition and Pearson correlation coefficient. Secondly, the data, after noise reduction, was converted into images, called snowflake images, according to symmetric polar coordinate method. Different fault types of axial piston pump can be identified by observing the snowflake images. After that, in order to evaluate the research results objectively, the obtained images were converted into Gray-Level Cooccurrence Matrixes. Their multiple eigenvalues were extracted, and the eigenvectors consisting of multiple eigenvalues were classified by Fuzzy C-Means clustering algorithm. Finally, according to the accuracy of classification results, the feasibility of applying the symmetric polar coordinate method to axial piston pump fault diagnosis has been validated.

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