Abstract
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.
Original language | English |
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Pages (from-to) | 517-525 |
Number of pages | 8 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 35 |
Early online date | 24 Apr 2014 |
DOIs | |
Publication status | E-pub ahead of print - 24 Apr 2014 |
Keywords
- block triangluar preconditioner
- convergence
- eigenvalues
- eigenvectors
- iterative method
- saddle point system