We consider linear ill-posed problems where both the operator and the right hand side are given approximately. For approximate solution of this equation we use the least error projection method. This method occurs to be a regularization method if the dimension of the projected equation is chosen properly depending on the noise levels of the operator and the right hand side. We formulate the monotone error rule for choice of the dimension of the projected equation and prove the regularization properties.
Ganina, A., Hamarik, U., & Kangro, U. (2014). On the Self-Regularization of Ill-Posed Problems by the Least Error Projection Method. Mathematical Modelling and Analysis, 19(3), 299-308. https://doi.org/10.3846/13926292.2014.923944
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