Implicit iteration methods in Hilbert scales under general smoothness conditions

摘要: For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In present paper regularized solutions obtained by implicit iteration in Hilbert scales. % By exploiting operator monotonicity of certain functions and interpolation techniques variable scales, we study these under general smoothness conditions. Order optimal error bounds given case parameter chosen either {\it a priori} or posteriori} discrepancy principle. realizing principle, fast algorithm proposed which based on Newton's method applied to properly transformed equations.