Comparison of convergence rates of the conjugate gradient method applied to various integral equation formulations

1988 ◽  
Author(s):  
J.E. Wheeler ◽  
D.R. Wilton
Keyword(s):  
Integral Equation ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convergence Rates

Conjugate Gradient Method for Estimation of Robin Coefficients

2014 ◽  
Vol 4 (2) ◽  
pp. 189-204 ◽  
Author(s):  
Yan-Bo Ma ◽  
Fu-Rong Lin
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Nonlinear Least Squares ◽  
Boundary Integral ◽  
Numerical Examples ◽  
Nonlinear Least Squares Problem ◽  
Ill Posed

AbstractWe consider a Robin inverse problem associated with the Laplace equation, which is a severely ill-posed and nonlinear. We formulate the problem as a boundary integral equation, and introduce a functional of the Robin coefficient as a regularisation term. A conjugate gradient method is proposed for solving the consequent regularised nonlinear least squares problem. Numerical examples are presented to illustrate the effectiveness of the proposed method.

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