Iterative Tikhonov regularization of tensor equations based on the Arnoldi process and some of its generalizations
| Autor: | Lothar Reichel, Fatemeh Panjeh Ali Beik, Mehdi Najafi–Kalyani |
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| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Iterative method Applied Mathematics Linear system 010103 numerical & computational mathematics Krylov subspace System of linear equations 01 natural sciences 010101 applied mathematics Tikhonov regularization Computational Mathematics Matrix (mathematics) Tensor product Applied mathematics 0101 mathematics Spectral method Mathematics |
| Zdroj: | Applied Numerical Mathematics. 151:425-447 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2020.01.011 |
| Popis: | We consider the solution of linear discrete ill-posed systems of equations with a certain tensor product structure. Two aspects of this kind of problems are investigated: They are transformed to large linear systems of equations and the conditioning of the matrix of the latter system is analyzed. Also, the distance of this matrix to symmetry and skew-symmetry is investigated. The aim of our analysis is to shed light on properties of linear discrete ill-posed problems and to study the feasibility of using Krylov subspace iterative methods in conjunction with Tikhonov regularization to solve Sylvester tensor equations with severely ill-conditioned coefficient matrices. The performance of several proposed algorithms is studied numerically. Applications include color image restoration and the solution of a 3D radiative transfer equation that is discretized by a Chebyshev collocation spectral method. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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