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Persistent URL http://purl.org/net/epubs/work/43562
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Record Id 43562
Title Trust-region and other regularisations of linear least-squares problems
Abstract We consider methods for regularising the least-square solutions of the linear system Ax=b. In particular, we propose iterative methods for solving large problems in which trust-region bound ||x||&It;triangle is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax-b||q(superscript)2(subscript) and a regularisation term ||x||(superscript)p(subscript)2 for various p and q = 1,2 is sought. In each case, one or more "secular" equations are derived, and fast Newton-like solution proceedures are suggested. The resulting slgorithms are available as part of the GALAHAD optimization library.
Organisation CSE , CSE-NAG , STFC
Keywords linear least-squares , regularisation , trust-region , secular equation , AMS classification , 65F22 , 65H05 , 65K05 , 90C25
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2008-005. 2008. cgtRALTR2008005.pdf 2008
Journal Article 2009. doi:10.1007/s10543-008-0206-8 2009