Abstract
This work studies a class of limited memory preconditioners (LMPs) for solving linear (positive-definite) systems of equations with multiple right-hand sides. We propose a class of (LMPs), whose construction requires a small number of linearly independent vectors. After exploring the theoretical properties of the preconditioners, we focus on three particular members: spectral-LMP, quasi-Newton-LMP, and Ritz-LMP. We show that the first two are well known, while the third is new. Numerical tests indicate that the Ritz-LMP is efficient on a real-life nonlinear optimization problem arising in a data assimilation system for oceanography.
Original language | English |
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Pages (from-to) | 912-935 |
Number of pages | 24 |
Journal | SIAM Journal on Optimization |
Volume | 21 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2011 |
Keywords
- Conjugate gradient
- Limited memory
- Linear systems
- Preconditioners