The Mathematical Institute, University of Oxford, Eprints Archive

Trust-region and other regularisations of linear least-squares problems

Cartis, Coralia and Gould, Nicholas I. M. and Toint, Philippe L. (2008) Trust-region and other regularisations of linear least-squares problems. Technical Report. Unspecified. (Submitted)

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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|| ≤ Δ is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax-b||2q and a regularisation term ||x||2p for various p and q=1,2 is sought. In each case, one of 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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1078
Deposited By:Lotti Ekert
Deposited On:06 May 2011 08:22
Last Modified:06 May 2011 08:22

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