scholarly journals Comparative studies of Tikhonov regularization and truncated singular value decomposition in the three-dimensional flame temperature field reconstruction

2015 ◽  
Vol 64 (24) ◽  
pp. 240201
Author(s):  
Xie Zheng-Chao ◽  
Wang Fei ◽  
Yan Jian-Hua ◽  
Cen Ke-Fa
Keyword(s):  
Temperature Field ◽  
Singular Value Decomposition ◽  
Tikhonov Regularization ◽  
Flame Temperature ◽  
Three Dimensional ◽  
Singular Value ◽  
Truncated Singular Value Decomposition ◽  
Field Reconstruction ◽  
Value Decomposition ◽  
Temperature Field Reconstruction

A New Modified SVD Method Applied in 3D Acoustic Temperature Field Reconstruction

2013 ◽  
Vol 732-733 ◽  
pp. 218-223 ◽  
Author(s):  
Wei Yang ◽  
Xiao Liang Zhu
Keyword(s):  
Temperature Field ◽  
Singular Value Decomposition ◽  
Singular Values ◽  
Singular Value ◽  
Temperature Fields ◽  
Time Data ◽  
Field Reconstruction ◽  
Value Decomposition ◽  
Svd Method ◽  
Temperature Field Reconstruction

In order to solve the ill-posed problem in 3D acoustic temperature field reconstruction, the paper proposed a new modified singular value decomposition (SVD) method.According to their reliability ,singular values were divided into three parts and got various degree of modification respectively. To verify the performance of the new algorithm based on the modified SVD method,two model temperature fields were reconstructed when the signal-to-noise ratio (SNR) of sound flight-time data was 50dB , 40dB and 30dB respectively.And the results were compared with those based on routine Truncated singular value decomposition (TSVD) and Tikhonov methods. Simulation results show that the new algorithm has higher precision, better anti-noise ability than the routine methods and it is more suitable for the complex temperature fields reconstruction, thus it is expected to be used for temperature field reconstruction on-line.

scholarly journals Reconstruction of Mercury’s internal magnetic field beyond the octupole

2021 ◽  
Author(s):  
Simon Toepfer ◽  
Ida Oertel ◽  
Vanita Schiron ◽  
Yasuhito Narita ◽  
Karl-Heinz Glassmeier ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Singular Value Decomposition ◽  
Tikhonov Regularization ◽  
High Performance ◽  
Singular Value ◽  
Internal Magnetic Field ◽  
Truncated Singular Value Decomposition ◽  
Reconstruction Methods ◽  
Value Decomposition ◽  
Spacecraft Data

Abstract. The reconstruction of Mercury’s internal magnetic field enables us to take a look into the inner heart of Mercury. In view of the BepiColombo mission, Mercury’s magnetosphere is simulated using a hybrid plasma code and the multipoles of the internal magnetic field are estimated from the virtual spacecraft data using three distinct reconstruction methods: the truncated singular value decomposition, the Tikhonov regularization and Capon’s minimum variance projection. The study shows that a precise determination of Mercury’s internal field beyond the octupole, up to the dotriacontapole is possible and that Capon’s method provides the same high performance as the Tikhonov regularization, which is superior to the performance of the truncated singular value decomposition.

scholarly journals A modified truncation singular value decomposition method for solving ill-posed problems

2018 ◽  
Vol 13 ◽  
pp. 174830181881360 ◽  
Author(s):  
Zhenyu Zhao ◽  
Riguang Lin ◽  
Zehong Meng ◽  
Guoqiang He ◽  
Lei You ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Method ◽  
Singular Value ◽  
Numerical Results ◽  
New Method ◽  
Truncated Singular Value Decomposition ◽  
Singular Value Decomposition Method ◽  
Ill Posed ◽  
Value Decomposition

A modified truncated singular value decomposition method for solving ill-posed problems is presented in this paper, in which the solution has a slightly different form. Both theoretical and numerical results show that the limitations of the classical TSVD method have been overcome by the new method and very few additive computations are needed.

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