An improved lopsided shift-splitting preconditioner for three-by-three block saddle point problems

• Jun Li ^[1] ; Xiangtuan Xiong ^[2]
  1. [1] Lanzhou University of Technology

     Lanzhou University of Technology

     China

     
  2. [2] Northwest Normal University

     Northwest Normal University

     China

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 1, 2025, págs. 131-144
• Idioma: inglés
• DOI: 10.33044/revuma.3672
• Enlaces
  • Texto completo
• Resumen

  • We consider an improved lopsided shift-splitting (ILSS) preconditioner for solving three- by-three block saddle point problems. This method enhances the work of Zhang et al. [Comput. Appl. Math. 41 (2022), 261]. We prove that the iteration method produced by the ILSS preconditioner is unconditionally convergent. Additionally, we show that all eigenvalues of the ILSS preconditioned matrix are real, with non-unit eigenvalues located in a positive interval. Numerical experiments demonstrate the effectiveness of the ILSS preconditioner.

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