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# Ill-posed problems with unbounded operators

@inproceedings{Ramm2002IllposedPW, title={Ill-posed problems with unbounded operators}, author={Alexander G. Ramm}, year={2002} }

- Published 2002

Let A be a linear, closed, densely defined unbounded operator in a Hilbert space. Assume that A is not boundedly invertible. If equation (1) Au = f is solvable, and ‖fδ−f‖ ≤ δ, then the following results are provided: problem Fδ(u) := ‖Au−fδ‖+α‖u‖ has a unique global minimizer uα,δ for any fδ, uα,δ = A∗(AA∗+ αI)fδ. There is a function α = α(δ), limδ→0 α(δ) = 0 such that limδ→0 ‖uα(δ),δ− y‖ = 0, where y is the unique minimal-norm solution to (1). A priori and a posteriori choices of α(δ) are… CONTINUE READING