Trust-region and other regularisations of linear least-squares problems |
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| Authors: | C Cartis N I M Gould P L Toint |
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| Institution: | (1) School of Mathematics, The King’s Buildings, University of Edinburgh, Edinburgh, EH9 3JZ, Scotland, UK;(2) Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, UK;(3) Department of Mathematics, Facultés Universitaires ND de la Paix–University of Namur, 61, rue de Bruxelles, 5000 Namur, Belgium |
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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‖2
q
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
ALAHAD optimization library.
This work was partially supported by EPSRC grants EP/E053351/1 and EP/F005369/1. |
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| Keywords: | Linear least-squares Regularisation Trust-region Secular equation |
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