摘要
本文变了一种思路在连续框架下采用二分法结合反迭代法来数值实现典则TSVD方法,就是先用最小二乘法直接求算子A的近似奇异系,转换为求对称正定广义特征值问题,再把对称正定广义特征值问题转化为对称特征值问题,最后求出cTSVD解。在连续框架下,通过数值结果相应得到一些结论,且结果显示在连续框架下有效数值实现典则TSVD方法时计算量小。
In this paper,a thought was changed to adopt the bisection method with inverse iteration to effectively realize canonical TSVD method in the continuous framework.In the continuous framework,firstly a approximate singular system for the operator A was solved,then it was changed to solve symmetric positive generalized eigenvalue problems,then it was changed to solve symmetric eigenvalue problems,lastly the cTSVD solution was solved.Some conclusions were got through the numerical results and the results show that the amount of calculation in the continuous framework is smaller than the amount of calculation in the discrete framework.
关键词
不适定问题
典则TSVD方法
最小二乘法
ill-posed problems
Canonical TSVD method
the least squares method.
