关于最小二乘问题近似解误差估计的进一步分析Further Study on the Error Estimates for Least Squares Problems
刘新国,张宏伟
摘要(Abstract)：
Brezinski等人给出了最小二乘问题近似解的一族误差估计。该误差估计含有1个实参数。本文的贡献有3个方面:其一是给出了1种参数选择策略;其二是对该族误差估计的性质做出进一步分析;其三是分析了应用于Tikhonov正则化时应注意的一些问题。
关键词(KeyWords)： 最小二乘;误差估计;Tikhonov正则化
基金项目(Foundation): 山东省自然科学基金项目(Y2008A07)资助
作者(Author): 刘新国,张宏伟
DOI: 10.16441/j.cnki.hdxb.2009.05.054
参考文献(References)：
- [1]Dahlquist G,Eisenstat S C,Golub G H.Boundsfor the error of linearsystems of equations using the theory of moments[J].J Math AnalAppl,1973,37(1):151-166.
- [2]Golub G H.Bounds for matrix moments[J].Rocky Mt J Math,1974,4(1):207-211.
- [3]Higham NJ.Accuracy and Stability of Numerical Algorithms[M].SIAM:Philadelphia,PA,1996.
- [4]Auchmuty G A.Posteriori error esti mates for linear equations[J].Numer Math,1992,61(1):1-6.
- [5]Galantai A.Astudy of Auchmuty’s error esti mates[J].ComputMath Appl,2001,42(7):1093-1102.
- [6]Brezinski C.Error esti mates for the solution of linear systems[J].SIAMJ Sci Comput,1999,21(2):764-781.
- [7]Brezinski C,Rodriguez G,Seatzu S.Error esti mates for linear sys-tems with applications to regularization[J].Numer Algor,2008,49(1):85-104.
- [8]Brezinski C,Rodriguez G,Seatzu S.Error esti mates for the regular-ization of least squares problems[J].Numer Algor,2009,51(1):61-76.
- [9]Hansen P C.Rank-Deficient and DiscreteⅢ-posed problems[M].Philadelphia:SIAM,1998.
- [10]Reichel L,Rodriguez G,Seatzu S.Error esti mates for ill-posedproblems[J].Numer Algor.2009,51(3):341-361.
文章评论(Comment)：
|
||||||||||||||||||
|
||||||||||||||||||