Ill-Conditioning and Regularization Techniques in Solutions of Linear Systems

2020 ◽  
pp. 57-87
Author(s):  
Eihab B. M. Bashier
Keyword(s):  
Linear Systems ◽  
Regularization Techniques ◽  
Ill Conditioning

scholarly journals Lightning Channel-Base Current Identification as Solution of a Volterralike Integral Equation

2008 ◽  
Vol 2 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Federico Delfino ◽  
Renato Procopio ◽  
Mansueto Rossi
Keyword(s):  
Integral Equation ◽  
Numerical Simulations ◽  
Time Domain ◽  
Measurement Noise ◽  
Induction Field ◽  
Base Current ◽  
Lightning Channel ◽  
Regularization Techniques ◽  
Ill Conditioning ◽  
The Time Domain

In this paper, a novel procedure to reconstruct the lightning channel-base current starting from the measurement of the induction field generated by it is presented. The procedure is based on a suitable mathematical manipulation of the equation expressing the induction field in the time domain, in order to transform it into a Volterra-like integral equation. Such kind of equations can be easily numerically solved without resorting to any sort of regularization techniques as they are not affected by the typical ill-conditioning of the inverse problems. The developed algorithm has been validated by means of several numerical simulations, which have shown its effectiveness also in presence of measurement noise on the induction field values.

Multi-parameter regularization techniques for ill-conditioned linear systems

2003 ◽  
Vol 94 (2) ◽  
pp. 203-228 ◽  
Author(s):  
C. Brezinski ◽  
M. Redivo-Zaglia ◽  
G. Rodriguez ◽  
S. Seatzu
Keyword(s):  
Linear Systems ◽  
Regularization Techniques ◽  
Parameter Regularization

A COMINRES-QLP Method for Solving Complex Symmetric Linear Systems

2020 ◽  
Vol 140 (12) ◽  
pp. 832-841
Author(s):  
Lijun Liu ◽  
Kazuaki Sekiya ◽  
Masao Ogino ◽  
Koki Masui
Keyword(s):  
Linear Systems ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric
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