Arnoldi process based on optimal estimation of the regularization parameter

2009 ◽  
Author(s):  
Xie Kai ◽  
Li Tong
Keyword(s):  
Regularization Parameter ◽  
Optimal Estimation ◽  
Arnoldi Process

Comparisons of regularization methods and regularization parameter selection methods in sound source identification using inverse boundary element method

2019 ◽  
Vol 67 (3) ◽  
pp. 219-227
Author(s):  
Youhong Xiao ◽  
Qingqing Song ◽  
Shaowei Li ◽  
Guoxue Lv ◽  
Zhenlin Ji
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Transfer Matrix ◽  
Sound Source ◽  
Source Identification ◽  
Regularization Parameter ◽  
Vibration Velocity ◽  
Regularization Methods ◽  
Inverse Boundary ◽  
Element Method

In noise source identification based on the inverse boundary element method (IBEM), the boundary vibration velocity is predicted based on the field pressure through a transfer matrix of the vibration velocity and field pressure established on the Helmholtz integral equation. Because the matrix is often ill-posed, it needs to be regularized before reconstructing the vibration velocity. Two regularization methods and two methods of selecting the regularization parameter are investigated through the simulation analysis of a pulsating sphere. The result of transfer matrix regularization is further verified through the reconstruction of the vibration of an aluminum plate. Additionally, to reduce the large errors at some frequencies in the reconstruction result, increasing the number of measuring points is more effective than reducing the distance between the measurement plane and the sound source.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document