期刊
BIT NUMERICAL MATHEMATICS
卷 49, 期 1, 页码 21-53出版社
SPRINGER
DOI: 10.1007/s10543-008-0206-8
关键词
Linear least-squares; Regularisation; Trust-region; Secular equation
资金
- EPSRC [EP/F005369/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/F005369/1] Funding Source: researchfish
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|| <= Delta is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax - b||(q)(2) 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 GALAHAD optimization library.
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