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Full Record Details
DOI
10.5286/raltr.2008005
Persistent URL
http://purl.org/net/epubs/work/43562
Record Status
Checked
Record Id
43562
Title
Trust-region and other regularisations of linear least-squares problems
Contributors
C Cartis
,
NIM Gould (STFC Rutherford Appleton Lab., and Oxford Univ.)
,
PL Toint
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
regularisation
,
65K05
,
65F22
,
90C25
,
secular equation
,
trust-region
,
AMS classification
,
65H05
,
linear least-squares
Funding Information
Related Research Object(s):
49215242
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Technical Reports
RAL-TR-2008-005. STFC, 2008.
cgtRALTR2008005.pdf
2008
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