Inexact rotated block triangular preconditioners for a class of block two-by-two matrices

Abstract

Based on rotated block triangular preconditioners proposed by Bai in (Sci China Math 56, 2013), we give a class of inexact rotated block triangular preconditioners for block two-by-two matrices of real square blocks $$W$$ and $$T$$ , which avoid inversion of the matrix $$\alpha W+T$$ exactly at each step of solving the linear systems. The spectral properties of the corresponding preconditioned matrices are analyzed. Numerical results show that these inexact rotated block triangular preconditioners are more effective than the exact ones when they are used to accelerate Krylov subspace iteration methods for solving block two-by-two linear systems.