The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods
DOI:
https://doi.org/10.29215/pecen.v6i0.1773Resumen
Here, m-order methods are developed that conserve the form of the first-order methods. The m-order methods have a higher rate of convergence than their first-order version. These m-order methods are subsequences of its precursor method, where some benefits of using vector and parallel processors can be explored. The numerical results obtained with vector implementations show computational advantages when compared to the first-order versions.Biografía del autor/a
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Gustavo Benitez Alvarez, Federal Fluminense UniversityUniversidade Federal Fluminense Centro Tecnológico Escola de Engenharia Industrial Metalúrgica de Volta Redonda Avenida dos Trabalhadores 420, Vila Santa Cecilia, Volta Redonda, Rio de Janeiro, Brasil. CEP 27255-250. Áreas: Física/Matemática/Engenharia
Referencias
Antuono M. and Colicchio G. (2016) Delayed Over-Relaxation for iterative methods. Journal of Computational Physics, 321: 892–907.
Apostol T.M. (1981) Mathematical analysis. Addilson-Wesley Publishing Company.
Bai Z.-Z. and Miao C.-Q. (2017) On local quadratic convergence of inexact simplified Jacobi–Davidson method. Linear Algebra and its Applications, 520: 215–241.
Bertaccini D. and Durastante F. (2018) Iterative methods and preconditioning for large and sparse linear systems with applications. Taylor & Francis Group.
Forsythe G.E. and Moler C.B. (1967) Computer solution of linear algebraic systems. Prentice-Hall, New Jersey.
Golub G.H. and Van Loan C. (2013) Matrix computations. The Johns Hopkins University Press, Baltimore, MD, 4th edition.
Golub G.H. and Varga R.S. (1961) Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II. Numerische Mathematik, 3: 147–168.
Kahan W.M. (1958) Gauss–Seidel methods of solving large systems of linear equations. PhD thesis, University of Toronto, Toronto.
Kepner J. (2009) Parallel MATLAB for Multicore and Multinode Computers. Society for Industrial and Applied Mathematics, USA, 1st edition.
Kolodziej S.P., Aznaveh M., Bullock M., David J., Davis T.A., Henderson M., Hu Y. and Sandstrom R. (2019) The SuiteSparse Matrix Collection Website Interface. Journal of Open Source Software, 4(35): 1244–1248.
Kong Q., Jing Y.-F., Huang T.-Z. and An H.-B. (2019). Acceleration of the Scheduled Relaxation Jacobi method: Promising strategies for solving large, sparse linear systems. Journal of Computational Physics, 397:108862.
Mazza M., Manni C., Ratnani A., Serra-Capizzano S. and Speleers H. (2019) Isogeometric analysis for 2D and 3D curl–div problems: Spectral symbols and fast iterative solvers. Computer Methods in Applied Mechanics and Engineering, 344: 970–997.
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