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

doi:10.1007/s42967-022-00222-0

Abstract

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.

Key words: Block triangular splitting, Block two-by-two linear systems, Eigenvalues, Preconditioner, flexible generalized minimal residual(FGMRES)

CLC Number:

65F10
65F08

Bo Wu, Xingbao Gao. Two-Parameter Block Triangular Splitting Preconditioner for Block Two-by-Two Linear Systems[J]. Communications on Applied Mathematics and Computation, 2023, 5(4): 1601-1615.

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