An optimal tri-vector iterative algorithm for solving ill-posed linear inverse problems

DOI10.1080/17415977.2012.717077zbMath1281.65100OpenAlexW2078317482MaRDI QIDQ2872715

Chein-Shan Liu

Publication date: 15 January 2014

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2012.717077

zbMATH Keywords

heat equationconjugate gradient methodLaplace equationconvergence rategeneralized minimal residual methodnumerical testinverse Cauchy problemlinear inverse problemsCalderón inverse probleminvariant-manifoldill-posed linear equations systemoptimal tri-vector iterative algorithm

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Nonlinear ordinary differential equations and systems (34A34) Heat equation (35K05) Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items (6)

A maximal projection solution of ill-posed linear system in a column subspace, better than the least squares solution ⋮ A double optimal descent algorithm for iteratively solving ill-posed linear inverse problems ⋮ Optimal algorithms in a Krylov subspace for solving linear inverse problems by MFS ⋮ A globally optimal tri-vector method to solve an ill-posed linear system ⋮ A doubly optimized solution of linear equations system expressed in an affine Krylov subspace ⋮ The homotopy method for identifying the radiative source term in the heat conduction problem

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