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计算数学  2013 

求解离散不适定问题的正则化GMERR方法

, PP. 195-204

Keywords: 不适定问题,正则化方法,GMERR方法,GMRES方法,GCV方法

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Abstract:

迭代极小残差方法是求解大型线性方程组的常用方法,通常用残差范数控制迭代过程.但对于不适定问题,即使残差范数下降,误差范数未必下降.对大型离散不适定问题,组合广义最小误差(GMERR)方法和截断奇异值分解(TSVD)正则化方法,并利用广义交叉校验准则(GCV)确定正则化参数,提出了求解大型不适定问题的正则化GMERR方法.数值结果表明,正则化GMERR方法优于正则化GMRES方法.

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