On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices
Jennifer Pestana · SIAM Journal on Matrix Analysis and Applications · 2014
Block lower triangular matrices and block upper triangular matrices are popular preconditioners for $2\times 2$ block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.