Convergence analysis of the homotopy perturbation method for solving nonlinear ill-posed operator equations

DOI10.1016/j.camwa.2010.08.069zbMath1219.65167OpenAlexW2030540937MaRDI QIDQ636624

Bo Han, Li Cao

Publication date: 28 August 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.08.069

zbMATH Keywords

convergence analysisiterative methodhomotopy perturbation methodnonlinear ill-posed operator equations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear ill-posed problems (47J06) Numerical methods for ill-posed problems for integral equations (65R30)

Related Items

Parameter estimation for metabolic networks with two stage Bregman regularization homotopy inversion algorithm ⋮ Numerical solution of fractional partial differential equations by numerical Laplace inversion technique ⋮ A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces ⋮ Rough surfaces reconstruction via phase and phaseless data by a multi-frequency homotopy iteration method ⋮ A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems ⋮ A new iteratively total variational regularization for nonlinear inverse problems ⋮ A new Kaczmarz-type method and its acceleration for nonlinear ill-posed problems ⋮ An accelerated Kaczmarz type method for nonlinear inverse problems in Banach spaces with uniformly convex penalty ⋮ A multigrid-homotopy method for nonlinear inverse problems ⋮ An accelerated sequential subspace optimization method based on homotopy perturbation iteration for nonlinear ill-posed problems ⋮ An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty ⋮ An accelerated homotopy-perturbation-Kaczmarz method for solving nonlinear inverse problems ⋮ An iteration regularization method with general convex penalty for nonlinear inverse problems in Banach spaces ⋮ Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method

Cites Work

• Unnamed Item
• Accelerated Landweber iterations for the solution of ill-posed equations
• A modified Landweber iteration for solving parameter estimation problems
• Homotopy perturbation method: a new nonlinear analytical technique
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Homotopy perturbation technique
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• A modified landweber method for inverse problems