Abstract
In this paper, we propose and analyze a projected homotopy perturbation method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces.
To expedite convergence, the approach uses two search directions given by homotopy perturbation iteration, and the new iteration is calculated as the projection of the current iteration onto the intersection of stripes decided by above directions.
The method allows to use
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 12271129
Award Identifier / Grant number: 12071184
Funding statement: The work of Y. Xia and B. Han are supported by the National Natural Science Foundation of China (No. 12271129). The work of W. Wang is supported by the National Natural Science Foundation of China (No. 12071184) and the Top-level Talent Project of Zhejiang Province.
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Articles in the same Issue
- Frontmatter
- Variation method solving of the inverse problems for Schrödinger-type equation
- Stability estimate for scalar image velocimetry
- Inverse problems for equations of a mixed parabolic-hyperbolic type with power degeneration in finding the right-hand parts that depend on time
- Inverse problem for integro-differential Kelvin–Voigt equations
- A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces
- Tensor tomography of the residual stress field in graded-index YAG’s single crystals
- Uniqueness and stability for inverse source problem for fractional diffusion-wave equations
- Reconstruction of modified transmission eigenvalues using Cauchy data
- Alternative fan-beam backprojection and adjoint operators
- The problem of determining multiple coefficients in an ultrahyperbolic equation
- A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube
- A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform
Articles in the same Issue
- Frontmatter
- Variation method solving of the inverse problems for Schrödinger-type equation
- Stability estimate for scalar image velocimetry
- Inverse problems for equations of a mixed parabolic-hyperbolic type with power degeneration in finding the right-hand parts that depend on time
- Inverse problem for integro-differential Kelvin–Voigt equations
- A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces
- Tensor tomography of the residual stress field in graded-index YAG’s single crystals
- Uniqueness and stability for inverse source problem for fractional diffusion-wave equations
- Reconstruction of modified transmission eigenvalues using Cauchy data
- Alternative fan-beam backprojection and adjoint operators
- The problem of determining multiple coefficients in an ultrahyperbolic equation
- A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube
- A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform