Geodesic
Implicit iterative scheme based on the pseudo-inversion algorithm and its application
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 1, pp. 117-129.

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A new version of the implicit iterative scheme is proposed for the implementation of which only matrix-vector computational procedures are required. This makes the proposed computational scheme potentially highly efficient for solving a wide class of high-dimensional problems on modern high-performance computing platforms, such as Nvidia Cuda. It is shown that the proposed algorithms can be used to solve ill-conditioned linear systems and least squares problems, as well as to construct iterative regularization algorithms. The results of computational experiments are presented, confirming the effectiveness of the proposed computational algorithms.
Keywords: implicit iterative scheme, simple iteration method, ill-conditioned problems, Ben–Israel iterative pseudo-inversion, iterative regularization, matrix-vector operations 
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A. I. Zhdanov; Yu. V. Sidorov. Implicit iterative scheme based on the pseudo-inversion algorithm and its application. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 1, pp. 117-129. http://geodesic.mathdoc.fr/item/VSGTU_2024_28_1_a6/

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