A Note on Preconditioning for Indefinite Linear Systems

2000/01/01 by Malcolm F. Murphy, Gene H. Golub, Andrew J. Wathen · 3 citations
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Matrix Theory and Algorithms

paper · doi:10.1137/s1064827599355153

openalex publication_date 2000/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

Preconditioners are often conceived as approximate inverses. For nonsingular indefinite matrices of saddle-point (or KKT) form, we show how preconditioners incorporating an exact Schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues. Thus approximations of the Schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses.

Citations

• Solution of Sparse Indefinite Systems of Linear Equations

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