Efficient estimation of regularization parameters via downsampling and the singular value expansion
نویسندگان
چکیده
منابع مشابه
Efficient Estimation of Regularization Parameters via Downsampling and the Singular Value Expansion Downsampling Regularization Parameter Estimation
The solution of the linear system of equations Ax ≈ b arising from the discretization of an ill-posed integral equation with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution x is found as the minimizer of J(x) = {‖Ax − b‖2 + λ‖Lx‖2} and depends on regularization parameter λ which trades off the fidelity of the solution data fit and its smoothing norm, determin...
متن کاملEfficient Estimation of Regularization Parameters via Downsampling and the Singular Value Expansion
The solution, x, of the linear system of equations Ax ≈ b arising from the discretization of an ill-posed integral equation g(s) = ∫ H(s, t)f(t) dt with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution x(λ) approximating the Galerkin coefficients of f(t) is found as the minimizer of J(x) = {‖Ax− b‖2 +λ‖Lx‖2}, where b is given by the Galerkin coefficients of g(...
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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2016
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-016-0637-6