Multilevel Jacobi and Gauss–Seidel type iteration methods for solving ill-posed integral equations
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Xingjun Luo
,
Wenyu Hu
Abstract
In this paper, multilevel Jacobi and Gauss–Seidel type iteration methods with compression technique are developed for solving ill-posed integral equations by making use of the multiscale structure of the matrix representation of the integral operator. The methods are based on the combination of Tikhonov regularization and multiscale Galerkin methods, and lead to fast solutions of discrete regularization methods for the equations. Choice for an a posteriori regularization parameter is proposed. An optimal convergence order for the method with the choices of parameters is established. Numerical experiments are given to illustrate the efficiency of the method.
Funding source: Natural Science Foundation of China
Award Identifier / Grant number: 11061001
Funding source: Natural Science Foundation of China
Award Identifier / Grant number: 11361005
Funding source: Science Foundation for Young Scholars of Jiangxi Provincial Education Department
Award Identifier / Grant number: GJJ-13647
Funding source: Jiangxi Provincial Natural Science Foundation of China
Award Identifier / Grant number: 20151BAB201011
Funding source: Jiangxi Provincial Natural Science Foundation of China
Award Identifier / Grant number: 20151BAB211014
Funding source: Gannan Normal University
Award Identifier / Grant number: 14zb21
The authors are grateful to the anonymous referees for their helpful comments and suggestions.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Identification of nonlinear heat conduction laws
- Numerical solution of the multidimensional Gelfand–Levitan equation
- On generalized cross validation for stable parameter selection in disease models
- An optimal regularization method for convolution equations on the sourcewise represented set
- Multilevel Jacobi and Gauss–Seidel type iteration methods for solving ill-posed integral equations
- Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance
- Asymptotic method for finding the coefficient of hydraulic resistance in lifting of fluid on tubing
- Identification of biological models described by systems of nonlinear differential equations
- Statistical inversion in electrical impedance tomography using mixed total variation and non-convex ℓp regularization prior
- Reconstruction of a convolution operator from the right-hand side on the semiaxis
- International workshop “Inverse Problems and Integral Geometry” Immanuel Kant Baltic Federal University, Kaliningrad, Russia October 13–16, 2014
Artikel in diesem Heft
- Frontmatter
- Identification of nonlinear heat conduction laws
- Numerical solution of the multidimensional Gelfand–Levitan equation
- On generalized cross validation for stable parameter selection in disease models
- An optimal regularization method for convolution equations on the sourcewise represented set
- Multilevel Jacobi and Gauss–Seidel type iteration methods for solving ill-posed integral equations
- Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance
- Asymptotic method for finding the coefficient of hydraulic resistance in lifting of fluid on tubing
- Identification of biological models described by systems of nonlinear differential equations
- Statistical inversion in electrical impedance tomography using mixed total variation and non-convex ℓp regularization prior
- Reconstruction of a convolution operator from the right-hand side on the semiaxis
- International workshop “Inverse Problems and Integral Geometry” Immanuel Kant Baltic Federal University, Kaliningrad, Russia October 13–16, 2014
