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

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...

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Publication date:
2008-02-05
URN:
uuid:291499c3-ea51-49b1-9c48-7c6becf001d7
Local pid:
oai:eprints.maths.ox.ac.uk:1078

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