求解线性系统和最小二乘问题的LSMR新形式

IF 0.5 Q4 ENGINEERING, MULTIDISCIPLINARY
Maryam Mojarrab, Afsaneh Hasanpour, Somayyeh Ghadamyari
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引用次数: 0

摘要

Fong和Saunders(2011)的最小二乘最小残差(LSMR)方法是一种求解线性系统Ax = b和最小二乘问题min∥Ax - b∥2的算法,其解析等效于应用于正常方程ATAx = AT b的MINRES方法,从而使数量∥ATrk∥2最小化(其中rk = b - Axk是当前迭代xk的残差)。该方法基于Golub-Kahan双对角化1过程,该过程生成标准正交的Krylov基向量。这里,在LSMR算法中实现了Golub-Kahan双对角化2过程。这种替换使算法比标准算法更简单。数值结果表明,新形式具有一定的竞争力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A new form of LSMR for solving linear systems and least-squares problems
The least squares minimal residual (LSMR) method of Fong and Saunders (2011) is an algorithm for solving linear systems Ax = b and least-squares problems min∥Ax - b∥2 that is analytically equivalent to the MINRES method applied to a normal equation ATAx = AT b so that the quantities ∥ATrk∥2 are minimised (where rk = b - Axk is the residual for current iterate xk). This method is based on the Golub-Kahan bidiagonalisation 1 process, which generates orthonormal Krylov basis vectors. Here, the Golub-Kahan bidiagonalisation 2 process is implemented in the LSMR algorithm. This substitution makes the algorithm simpler than the standard algorithm. Also, numerical results show the new form to be competitive.
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CiteScore
1.30
自引率
0.00%
发文量
37
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