Geodesic
Implicit iterative schemes based on~singular decomposition and regularizing algorithms
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 3, pp. 549-556

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A new version of the simple iterations implicit method based on the singular value decomposition is proposed. It is shown that this variant of the simple iterations implicit method can significantly improve the computational stability of the algorithm and at the same time provides a high rate of its convergence. The application of the simple iterations implicit method based on the singular value decomposition for the development of iterative regularization algorithms is considered. The proposed algorithms can be effectively used to solve a wide class of ill-posed and ill-conditioned computational problems.
Keywords: implicit iterative schemes, computational stability of iterative schemes, iterative regularization methods.
Mots-clés : singular value decomposition, convergence rate 
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     author = {A. I. Zhdanov},
     title = {Implicit iterative schemes based on~singular decomposition and regularizing algorithms},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {549--556},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2018_22_3_a8/}
}
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A. I. Zhdanov. Implicit iterative schemes based on~singular decomposition and regularizing algorithms. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 3, pp. 549-556. http://geodesic.mathdoc.fr/item/VSGTU_2018_22_3_a8/