@techreport{NA-08/02,
  abstract = "We consider methods for regularising the least-squares solution of the linear system&nbsp;<em>Ax = b</em>. In particular, we propose iterative methods for solving large problems in which a trust-region bound<em>||x|| &le; &Delta;</em>&nbsp;is imposed on the size of the solution, and in which the least value of linear combinations of&nbsp;<em>||Ax-b||</em><sub>2</sub><sup>q</sup>&nbsp;and a regularisation term&nbsp;<em>||x||</em><sub>2</sub><sup>p</sup>&nbsp;for various&nbsp;<em>p</em>&nbsp;and&nbsp;<em>q</em>=1,2 is sought. In each case, one of more &quot;secular&quot; equations are derived, and fast Newton-like solution procedures are suggested. The resulting algorithms are available as part of the GALAHAD optimization library.",
  author = "Coralia Cartis and Nicholas I. M. Gould and Philippe L. Toint",
  institution = "Oxford University Computing Laboratory",
  month = "February",
  number = "NA-08/02",
  title = "Trust-region and other regularisations of linear least-squares problems",
  year = "2008",
}