A new version of KSOR method with lower number of iterations and lower spectral radius

  • R. Constantinescu
  • R. C. Poenaru
  • F. Pop
  • P. G. PopescuEmail author
Methodologies and Application


In this paper, we propose a new method for solving linear algebraic systems based on the KSOR method. The new approach introduces a new coefficient in the assumed updated section from the KSOR method. It obtains the same solution as KSOR for a given linear algebraic system, but in order to get this, we have to modify the diagonal of the coefficient matrix of the initial system. The new method reaches the solution in fewer steps than KSOR on certain examples, but we have an additional step for the modification mentioned above with O(m) complexity, while a normal step of iteration has \(O(m^2)\) complexity, so overall our method has better performances than KSOR method. Furthermore, on certain examples, the spectral radius of the iteration matrix of the new method is strictly less than the one of KSOR and MKSOR methods.


Linear algebraic systems Iterative methods Iteration matrices Spectral radius 



This study was funded by the Sectoral Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/134398. The research presented in this paper is also supported by the following projects: NETIO - ForestMon (53/05.09.2016, cod SMIS2014+ 105976), SPERO (PN-III-P2-2.1-SOL-2016-03-0046, 3Sol/2017) and ROBIN (PN-III-P1-1.2-PCCDI-2017-0734).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Computer Science and Engineering Department, Faculty of Automatic Control and ComputersUniversity “Politehnica” of BucharestBucharest (6)Romania

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