The generalized singular value decomposition and the general (A-λB)-problem

1984 ◽  
Vol 24 (4) ◽  
pp. 568-583 ◽  
Author(s):  
Bo Kågström
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Generalized Singular Value Decomposition ◽  
Value Decomposition

scholarly journals Application of generalized singular value decomposition to ionospheric tomography

2004 ◽  
Vol 22 (10) ◽  
pp. 3437-3444 ◽  
Author(s):  
K. Bhuyan ◽  
S. B. Singh ◽  
P. K. Bhuyan
Keyword(s):  
Singular Value Decomposition ◽  
Regularization Parameter ◽  
Singular Value ◽  
Electron Content ◽  
Generalized Singular Value Decomposition ◽  
Total Electron ◽  
Ionospheric Tomography ◽  
Low Latitude Ionosphere ◽  
A Chain ◽  
Value Decomposition

Abstract. The electron density distribution of the low- and mid-latitude ionosphere has been investigated by the computerized tomography technique using a Generalized Singular Value Decomposition (GSVD) based algorithm. Model ionospheric total electron content (TEC) data obtained from the International Reference Ionosphere 2001 and slant relative TEC data measured at a chain of three stations receiving transit satellite transmissions in Alaska, USA are used in this analysis. The issue of optimum efficiency of the GSVD algorithm in the reconstruction of ionospheric structures is being addressed through simulation of the equatorial ionization anomaly (EIA), in addition to its application to investigate complicated ionospheric density irregularities. Results show that the Generalized Cross Validation approach to find the regularization parameter and the corresponding solution gives a very good reconstructed image of the low-latitude ionosphere and the EIA within it. Provided that some minimum norm is fulfilled, the GSVD solution is found to be least affected by considerations, such as pixel size and number of ray paths. The method has also been used to investigate the behaviour of the mid-latitude ionosphere under magnetically quiet and disturbed conditions.

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