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Two-Parameter Block Triangular Splitting Preconditioner for Block Two-by-Two Linear Systems

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Abstract

This paper proposes a two-parameter block triangular splitting (TPTS) preconditioner for the general block two-by-two linear systems. The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions. The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual (FGMRES) method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, Ningxia, China

    Bo Wu

  2. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710062, Shaanxi, China

    Xingbao Gao

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  1. Bo Wu
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  2. Xingbao Gao
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Correspondence to Bo Wu.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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This work is supported by the National Natural Science Foundation of China under Grant Nos. 61273311 and 61803247.

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Wu, B., Gao, X. Two-Parameter Block Triangular Splitting Preconditioner for Block Two-by-Two Linear Systems. Commun. Appl. Math. Comput. 5, 1601–1615 (2023). https://doi.org/10.1007/s42967-022-00222-0

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