Abstract
We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x|| <= Delta is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax - b||(q)(2) and a regularisation term ||x||(2)(p) for various p and q = 1, 2 is sought. In each case, one or more "secular" equations are derived, and fast Newton-like solution procedures are suggested. The resulting algorithms are available as part of the GALAHAD optimization library.
Original language | English |
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Pages (from-to) | 21-53 |
Number of pages | 33 |
Journal | Bit numerical mathematics |
Volume | 49 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2009 |
Keywords / Materials (for Non-textual outputs)
- Linear least-squares
- Regularisation
- Trust-region
- Secular equation
- CONJUGATE-GRADIENT METHOD
- GLOBAL PERFORMANCE
- REGULARIZATION
- OPTIMIZATION
- ALGORITHM
- EQUATIONS
- LSQR