Convergence of Regularization Parameters for Solutions Using the Filtered Truncated Singular Value Decomposition

摘要: The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires estimation a parameter that balances between sizes fit data function term. unbiased predictive risk estimator is one suggested method for finding when noise measurements normally distributed known variance. In this paper we provide an algorithm using automatically finds both number terms use from decomposition. Underlying new result proves converges For analysis it sufficient assume Picard condition satisfied exact completely contaminates measured coefficients sufficiently large terms, dependent on level degree ill-posedness system. A lower bound provided leading computationally efficient algorithm. Supporting results are compared those obtained generalized cross validation. Simulations two-dimensional examples verify theoretical effectiveness increasing levels, demonstrate relative reconstruction errors less than This pre-print article published BIT Numerical Mathematics. final authenticated version available online at: https URL.