Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations

In this paper we consider the classical Kaczmarz algorithm for solving system of linear equations. Based on the geometric relationship between the error vector and rows of the coefficient matrix, we derive the optimal strategy of selecting rows at each step of the algorithm for solving consistent sy...

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Detalles Bibliográficos
Autores principales: Huang, Xinyin, Liu, Gang, Niu, Qiang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7302833/
http://dx.doi.org/10.1007/978-3-030-50417-5_17
Descripción
Sumario:In this paper we consider the classical Kaczmarz algorithm for solving system of linear equations. Based on the geometric relationship between the error vector and rows of the coefficient matrix, we derive the optimal strategy of selecting rows at each step of the algorithm for solving consistent system of linear equations. For solving perturbed system of linear equations, a new upper bound in the convergence rate of the randomized Kaczmarz algorithm is obtained.

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